Exhibit 24
                               Power of Attorney

         Know all by these presents, that the undersigned hereby makes,
constitutes and appoints each of Melinda Lackey and Michael Wong, or either of
them acting singly, and with full power of substitution and re-substitution,
the undersigned's true and lawful attorney-in-fact (each of such persons and
their substitutes being referred to herein as the "Attorney-in-Fact"), with full
power to act for the undersigned and in the undersigned's name, place and stead,
in any and all capacities, to:

   1.    Prepare, execute, and submit to the Securities and Exchange Commission
      ("SEC") a Form ID, including amendments thereto, and any other documents
       necessary or appropriate to obtain codes and passwords enabling the
       undersigned to make electronic filings with the SEC of reports required
       or considered by the Attorney-in-Fact to be advisable under Section 13 or
       Section 16 of the Securities Exchange Act of 1934 (the "Exchange Act") or
       any rule or regulation of the SEC;

   2.    Prepare, execute and submit to the SEC, Alaunos Therapeutics, Inc.
      (including any successor or assign, the "Company"), and/or any national
      securities exchange on which the Company's securities are listed any and
      all reports (including any amendments thereto) the undersigned is required
      to file with the SEC, or which the Attorney-in-Fact considers it advisable
      to file with the SEC, under Section 13 or Section 16 of the Exchange Act
      or any rule or regulation thereunder, or under Rule 144 under the
      Securities Act of 1933 ("Rule 144"), with respect to the any security of
      the Company, including Forms 3, 4 and 5, Schedules 13D and 13G, and Forms
      144; and

   3.    Obtain, as the undersigned's representative and on the undersigned's
      behalf, information regarding transactions in the Company's equity
      securities from any third party, including the Company and any brokers,
      dealers, employee benefit plan administrators and trustees, and the
      undersigned hereby authorizes any such third party to release any such
      information to the Attorney-in-Fact.

     The undersigned acknowledges that:

         a)     This Power of Attorney authorizes, but does not require, the
             Attorney-in-Fact to act in his or her discretion on information
             provided to such Attorney-in-Fact without independent verification
             of such information;

        b)     Any documents prepared or executed by the Attorney-in-Fact on
            behalf of the undersigned pursuant to this Power of Attorney will be
            in such form and will contain such information as the
            Attorney-in-Fact, in his or her discretion, deems necessary or
            desirable;

        c)     Neither the Company nor the Attorney-in-Fact assumes any
            liability for the undersigned's responsibility to comply with the
            requirements of Section 13 or Section 16 of the Exchange Act or Rule
            144, any liability of the undersigned for any failure to comply with
            such requirements, or any liability of the undersigned for
            disgorgement of profits under Section 16(b) of the Exchange Act; and

       d)      This Power of Attorney does not relieve the undersigned from
            responsibility for compliance with the undersigned's obligations
            under Section 13 or Section 16 of the Exchange Act, including,
            without limitation, the reporting requirements under Section 13 or
            Section 16 of the Exchange Act.

     The undersigned hereby grants to the Attorney-in-Fact full power and
authority to do and perform each and every act and thing requisite, necessary or
advisable to be done in connection with the foregoing, as fully, to all intents
and purposes, as the undersigned might or could do in person, hereby ratifying
and confirming all that the Attorney-in-Fact, or his or her substitute or
substitutes, shall lawfully do or cause to be done by authority of this Power of
Attorney.

     This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 4 or 5 or Schedules 13D or 13G
or Forms 144 with respect to the undersigned's holdings of and transactions in
securities of the Company, unless earlier revoked by the undersigned in a signed
writing delivered to the Attorney-in-Fact. This Power of Attorney revokes all
previous powers of attorney with respect to the subject matter of this Power of
Attorney.

     The signature may be delivered via facsimile, electronic mail (including
any electronic signature covered by the U.S. federal ESIGN Act of 2000, Uniform
Electronic Transactions Act, the Electronic Signatures and Records Act or other
applicable law, e.g., www.docusign.com) or other transmission method and any
signature so delivered shall be deemed to have been duly and validly delivered
and be valid and effective for all purposes.

     IN WITNESS WHEREOF, the undersigned has executed this Power of Attorney as
of June 27, 2022.

                                                 Jaime Vieser

                                                 /s/ Jaime Vieser
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                                                     Signature