Exhibit 99.1

August 26, 2021

RMR Mortgage Trust

Two Newton Place

255 Washington Street, Suite 300

Newton, Massachusetts 02458

Ladies and Gentlemen:

Reference is made to that certain Agreement and Plan of Merger (the “Merger Agreement”), dated as of April 26, 2021, by and between RMR Mortgage Trust (“RMRM”) and Tremont Mortgage Trust (“TRMT”). Capitalized terms used in this letter agreement without definition shall have the meanings given therefor in the Merger Agreement.

With reference to and as permitted and required by Sections 6.1(a)(iii), 6.1(a)(xv) and 6.1(a) (last paragraph) of the Merger Agreement, TRMT must declare and pay a distribution to the holders of TRMT Common Shares in the amount of $0.17 per TRMT Common Share (the “TRMT Distribution”) prior to the Merger Effective Time, with such distribution being subject to the consent of RMRM (not to be unreasonably conditioned, withheld or delayed).

The purpose of this letter agreement is to confirm the following:

1. That RMRM consents to the declaration and payment by TRMT of the TRMT Distribution to be paid prior to the Merger Effective Time, subject to the condition that, with reference to and as permitted by Section 6.2(a)(iii) of the Merger Agreement, RMRM will declare and pay (contemporaneously with the declaration and payment of the TRMT Distribution and prior to the Merger Effective Time) a distribution to the holders of RMRM Common Shares in the amount of $0.15 per RMRM Common Share (the “RMRM Distribution” and, together with the TRMT Distribution, the “Distributions”); provided, further that the parties acknowledge and agree that the TRMT Distribution, in part, and the RMRM distribution shall be in lieu of the regular quarterly cash distribution to be paid by TRMT and RMRM, respectively, with respect to the third quarter of calendar year 2021 and no such quarterly distribution for the third quarter shall be required by either TRMT or RMRM.

2. That, in connection with the Distributions and with reference to and as required by Sections 3.1 and 3.5 of the Merger Agreement, the Exchange Ratio is hereby adjusted to 0.516 of one (1) RMRM Common Share for each TRMT Common Share.

3. That, notwithstanding Section 2.2 of the Merger Agreement and subject to receipt of the RMRM Shareholder Approval and the TRMT Shareholder Approval and the satisfaction or waiver of each of the other conditions to Closing set forth in Article 8 of the Merger Agreement, the Closing Date is hereby scheduled for September 30, 2021.

TRMT and RMRM each acknowledges and agrees, by signing this letter agreement, that the Merger Agreement is in full force and effect and each party has complied with its obligations thereunder with respect to the matters referenced herein. Except as expressly provided herein, this letter agreement shall not amend, modify, alter or waive in any respect any other agreements, rights or obligations of TRMT or RMRM under or in respect of the Merger Agreement.

Sincerely,

TREMONT MORTGAGE TRUST

By:	/s/ G. Douglas Lanois
	G. Douglas Lanois
	Chief Financial Officer and Treasurer

Accepted and agreed to as of the date set forth above:

RMR MORTGAGE TRUST

By:	/s/ Thomas J. Lorenzini
	Thomas J. Lorenzini
	President