EX-99.(a)(1)(G)

This announcement is neither an offer to purchase nor a solicitation of an offer to sell Shares (as defined below). The Offer (as defined below) is made solely by the Offer to Purchase, dated March 25, 2016, and the related Letter of Transmittal and any amendments or supplements thereto. The Offeror (as defined below) is not aware of any state where the making of the Offer is prohibited by any administrative or judicial action pursuant to any valid state statute. If the Offeror becomes aware of any valid state statute prohibiting the making of the Offer or the acceptance of the Shares pursuant thereto, the Offeror will make a good faith effort to comply with that state statute or seek to have such statute declared inapplicable to the Offer. If, after a good faith effort, the Offeror cannot do so, the Offeror will not make the Offer to, nor will tenders be accepted from or on behalf of, the holders of Shares in that state. Except as set forth above, the Offer is being made to all holders of Shares.

Pomegranate Merger Sub, Inc., a Delaware corporation (the “Offeror” or “we”) and a wholly owned subsidiary of Pomegranate Holdings, Inc., a Delaware corporation (“Parent”), is offering to purchase all of the issued and outstanding shares of common stock, par value $0.01 per share (the “Shares”), of The Fresh Market, Inc., a Delaware corporation (“The Fresh Market”), at a purchase price of $28.50 per Share, net to the holders thereof, payable in cash (the “Offer Price”), without interest, less any applicable tax withholding, upon the terms and subject to the conditions set forth in the Offer to Purchase, dated March 25, 2016 (the “Offer to Purchase”), and in the related Letter of Transmittal (the “Letter of Transmittal” which, together with the Offer to Purchase, as each may be amended or supplemented from time to time, in accordance with the Merger Agreement described below, collectively constitute the “Offer”). Following the consummation of the Offer, and subject to the conditions described in the Offer to Purchase, the Offeror intends to effect the Merger described below.

THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE AT 12:00 MIDNIGHT,

NEW YORK CITY TIME, ON APRIL 21, 2016 (ONE MINUTE AFTER 11:59 P.M.,

NEW YORK CITY TIME, ON APRIL 21, 2016), UNLESS THE OFFER IS EXTENDED.

The purpose of the Offer is for Parent, through the Offeror, to acquire control of, and the entire equity interest in, The Fresh Market. Parent is controlled by certain equity funds managed by Apollo Management VIII, L.P. (“Management VIII”).

The Offer is being made in connection with the Agreement and Plan of Merger, dated as of March 11, 2016, by and among The Fresh Market, Parent and the Offeror (as it may be amended from time to time, the “Merger Agreement”), pursuant to which, after the completion of the Offer and the satisfaction or waiver of certain conditions, the Offeror will merge with and into The Fresh Market, with The Fresh Market surviving as a wholly owned subsidiary of Parent (the “Merger”), and each outstanding Share (other than Shares subject to forfeiture conditions, Shares owned by The Fresh Market as treasury stock and Shares owned by any stockholders of The Fresh Market who have properly exercised appraisal rights under Section 262 of the General Corporation Law of the State of Delaware (the “DGCL”) will be automatically canceled and converted into the right to receive an amount in cash equal to the Offer Price, without interest and less any applicable tax withholding. As a result of the Merger, the Shares will cease to be publicly traded, and The Fresh Market will become a wholly owned subsidiary of Parent. Ray Berry and Brett Berry, who collectively own approximately 9.8% of the Shares, have agreed to exchange a portion of their Shares (the “Rollover Shares”) pursuant to the Rollover, Contribution and Exchange Agreement dated as of March 12, 2016 (the “Rollover Agreement”), by and among the stockholders affiliated with Ray Berry and Brett Berry party thereto (collectively, the “Rollover Stockholders”) and Parent, for an indirect equity interest in Parent, and have agreed not to tender the Rollover Shares in the Offer. The Offer, the Merger and the other transactions contemplated by the Merger Agreement, but excluding, in any event, the related financing, are collectively referred to as the “Transactions.” The Merger Agreement is more fully described in Section 11 — “Purpose of the Offer and Plans for The Fresh Market; Transaction Documents” of the Offer to Purchase.

The Offer is not subject to any financing condition. The Offer is conditioned upon, among other things, the following: (a) the number of Shares validly tendered and not properly withdrawn in accordance with the terms of the Offer, excluding any Shares tendered pursuant to guaranteed delivery procedures that have not yet been “received” by the American Stock Transfer & Trust Company, LLC, (the “Depositary and Paying Agent”), together with the Shares then owned by the Offeror, other than Rollover Shares, represents at least one share more than 50% of the then-outstanding Shares (the “Minimum Condition”); (b) the expiration or early termination of the waiting period applicable to the Offer and the Merger under the Hart-Scott-Rodino Antitrust Improvements Act of 1976, as amended (the “HSR Act”); and (c) subject to certain exceptions, the absence, since March 11, 2016, of any effect, change, event or occurrence that, individually or in the aggregate, has had or would reasonably be expected to have a Material Adverse Effect (as defined in the Merger Agreement). The Offer is also subject to certain other terms and conditions. See Section 13 — “Conditions of the Offer.”

The offering period of the Offer will expire at the Expiration Time. The term “Expiration Time” means 12:00 midnight, New York City time, on April 21, 2016 (one minute after 11:59 P.M. New York City time, on April 21, 2016), unless the Offeror, in accordance with the Merger Agreement, has extended the offering period of the Offer, in which event the term “Expiration Time” will mean the latest time and date at which the offering period of the Offer, as so extended by the Offeror, will expire. Shares tendered pursuant to the Offer may be withdrawn by following the procedures set forth in Section 4 — “Withdrawal Rights” of the Offer to Purchase for withdrawing Shares in a timely manner, at any time on or prior to the Expiration Time, and, if not previously accepted for payment at any time, after May 24, 2016 pursuant to Securities and Exchange Commission (“SEC”) regulations.

The Board of Directors of The Fresh Market (with the exception of Ray Berry, who recused himself from the Board meeting and all Board deliberations on the Transactions) has unanimously (a) determined that the Transactions are fair to and in the best interests of The Fresh Market and its stockholders (other than the Rollover Stockholders), (b) declared the Merger Agreement and the Transactions advisable and (c) recommended that The Fresh Market’s stockholders tender their Shares in the Offer.

If as a result of the Offer, the Offeror holds Shares (other than Rollover Shares) that represent at least one Share more than 50% of all the issued and outstanding Shares, Parent, the Offeror and The Fresh Market will, subject to the satisfaction or waiver of the remaining conditions set forth in the Merger Agreement, as soon as practicable, consummate the Merger under the provisions of Section 251(h) of the DGCL without prior notice to, or any action by, any other stockholder of The Fresh Market. We expect the Merger to occur without a “subsequent offering period” within the meaning of Rule 14d-11 under the Securities Exchange Act of 1934. We do not expect there to be a significant period of time between the consummation of the Offer and the consummation of the Merger.

Provided that the Merger Agreement has not been terminated in accordance with its terms, if at the scheduled Expiration Time of the Offer any of the conditions to the Offer have not been satisfied or waived, Parent will cause the Offeror to extend the Offer to permit the satisfaction of all Offer Conditions (as set forth in Section 13 — “Conditions of the Offer” of the Offer to Purchase, the “Offer Conditions”), except that, in certain circumstances, if the sole remaining unsatisfied Offer Condition is the Minimum Condition, the Offeror will only be permitted to extend the Offer on up to two occasions of 5 business days each (or such other duration as Parent and The Fresh Market may agree) unless The Fresh Market requests the Offeror to further extend the Offer. If the debt financing is not available at the scheduled Expiration Time of the Offer and all the Offer Conditions are satisfied, the Offeror may, subject to certain conditions, extend the Offer on up to four occasions of 5 business days each (or such other duration as Parent and The Fresh Market may agree). The Merger Agreement also provides that the Offeror will, provided that the Merger Agreement has not been terminated in accordance with its terms, extend the Offer for any period required by any applicable law, interpretation or position of the SEC or its staff or Nasdaq Global Select Market (“NASDAQ”).

The Offeror is not, however, required to extend the Offer or the Expiration Time beyond the Outside Date. The Outside Date is July 9, 2016, except that if the marketing period for Parent’s debt financing has commenced, but the Shares tendered in the Offer have not been accepted for payment, then the Outside Date will be automatically extended to the date that is five business days following the then-scheduled end date of the marketing period (which will not be later than August 4, 2016).

Any extension, termination or amendment of the Offer will be followed as promptly as practicable by public announcement thereof, and such announcement in the case of an extension will be made no later than 9:00 A.M., New York City time, on the next business day after the previously scheduled Expiration Time of the Offer.

The Offeror expressly reserves the right (but is not obligated) to increase the Offer Price, to waive any Offer Condition or to make any other changes in the terms and conditions of the Offer; provided that the Minimum Condition and certain other terms and conditions of the Offer described in the Offer to Purchase may be waived or modified by the Offeror only with the prior written consent of The Fresh Market.

In order to tender your Shares in the Offer, you must (a) follow the procedures described in Section 3 — “Procedures for Tendering Shares” of the Offer to Purchase or (b) if your Shares are held through a broker, dealer, commercial bank, trust company or other nominee, contact such nominee and request that they effect the transaction for you and tender your Shares. If your Shares are held through a broker, dealer, commercial bank, trust company or other nominee, you must contact such broker, dealer, commercial bank, trust company or other nominee to tender your Shares. If you desire to tender Shares, and certificates evidencing your Shares are not immediately available, or if you cannot comply with the procedures for book-entry transfer described in the Offer to Purchase on a timely basis, or if you cannot deliver all required documents to our Depositary and Paying Agent prior to the expiration of our Offer, you may tender your Shares by following the procedures for guaranteed delivery set forth in Section 3 of the Offer to Purchase.

For purposes of the Offer, the Offeror will be deemed to have accepted for payment and thereby to have purchased Shares validly tendered and not properly withdrawn if and when the Offeror gives oral or written notice to the Depositary and Paying Agent of its acceptance for payment of those Shares pursuant to the Offer. Payment for Shares accepted for payment pursuant to the Offer will be made by depositing the Offer Price with the Depositary and Paying Agent, which will act as agent for tendering stockholders for the purpose of receiving payments from the Offeror and transmitting such payments to tendering stockholders. Under no circumstances will interest be paid on the Offer Price for Shares, regardless of any extension of the Offer or any delay in making payment for Shares.

Shares tendered pursuant to the Offer may be withdrawn at any time on or prior to the Expiration Time, and, if not previously accepted for payment at any time, after May 24, 2016, the date that is 60 days after the date of the commencement of the Offer, pursuant to SEC regulations. For your withdrawal to be effective, a written (or, with respect to Eligible Institutions (as defined in the Offer to Purchase), a facsimile transmission) notice of withdrawal with respect to the Shares must be timely received by the Depositary and Paying Agent at one of its addresses set forth on the back cover of the Offer to Purchase, and the notice of withdrawal must specify the name of the person who tendered the Shares to be withdrawn, the number of Shares to be withdrawn and the name of the registered holder of the Shares to be withdrawn, if different from that of the person who tendered such Shares. The signature(s) on the notice of withdrawal must be guaranteed by an Eligible Institution, unless those Shares have been tendered for the account of any Eligible Institution. If Shares have been tendered pursuant to the procedures for book-entry transfer, any notice of withdrawal must specify the name and number of the account at The Depository Trust Company (“DTC”) to be credited with the withdrawn Shares. If certificates representing the Shares to be withdrawn have been delivered or otherwise identified to the Depositary and Paying Agent, the name of the registered owner and the serial numbers shown on such certificates must also be furnished to the Depositary and Paying Agent prior to the physical release of such certificates. If you tender Shares by giving instructions to a broker, dealer, commercial bank, trust company or other nominee, you must instruct such broker, dealer, commercial bank, trust company or other nominee to arrange for the withdrawal of your Shares.

All questions as to the form and validity (including time of receipt) of a tender or a notice of withdrawal will be determined by the Offeror, in its sole discretion, which determination will be final and binding absent a finding to the contrary by a court of competent jurisdiction. No tender or withdrawal of Shares will be deemed to have been validly made until all defects and irregularities have been cured or waived. None of Parent, the Offeror or any of their respective affiliates or assigns, the Depositary and Paying Agent, D.F. King & Co., Inc. (the “Information Agent”), or any other person will be under any duty to give notification of any defects or irregularities in any tender of Shares or notice of withdrawal or incur any liability for failure to give such notification. Withdrawals of tenders of Shares may not be rescinded, and any Shares properly withdrawn will be deemed not to have been validly tendered for purposes of the Offer. However, withdrawn Shares may be retendered by following one of the procedures for tendering Shares described in the Offer to Purchase at any time prior to the Expiration Time.

The receipt of cash in exchange for Shares pursuant to the Offer and the Merger generally will be taxable for U.S. federal income tax purposes, generally will be taxable under applicable state and local tax laws, and may be taxable under other tax laws. All Fresh Market stockholders should consult with their tax advisors as to the particular tax consequences to them of the Offer and the Merger.

The information required to be disclosed by paragraph (d)(1) of Rule 14d-6 of the General Rules and Regulations under the Exchange Act is contained in the Offer to Purchase and is incorporated herein by reference.

Upon the request of the Offeror, The Fresh Market has provided to the Offeror its list of stockholders and security position listings for the purpose of disseminating the Offer to holders of Shares. The Offer to Purchase and the related Letter of Transmittal are being mailed to record holders of Shares and will be furnished to brokers, dealers, commercial banks, trust companies and other nominees whose names, or the names of whose nominees, appear on the stockholder list or, if applicable, who are listed as participants in a clearing agency’s security position listing, for subsequent transmittal to beneficial owners of Shares.

The Offer to Purchase, the related Letter of Transmittal and The Fresh Market’s Solicitation/Recommendation Statement on Schedule 14D-9 (which contains the recommendation of The Fresh Market’s Board of Directors and the reasons therefor) contain important information that should be read carefully before any decision is made with respect to the Offer.

Questions and requests for assistance and copies of the Offer to Purchase, the Letter of Transmittal and all other tender offer materials may be directed to the Information Agent at its address and telephone number set forth below and will be furnished promptly at the Offeror’s expense. Neither Parent nor the Offeror will pay any fees or commissions to any broker, dealer, commercial bank, trust company or other nominee (other than to the Depositary and Paying Agent and the Information Agent) in connection with the solicitation of tenders of Shares pursuant to the Offer.