POWER OF ATTORNEY


       Know all by these presents, that the undersigned hereby constitutes and
appoints Megan Filoon, of Molecular Templates, Inc. (the "Company"), and Matthew
J. Gardella, Zachary Liebnick, Meg Green, Anne Leland, Brenda Meyette and
Jacquelyn Cannata, each of Mintz, Levin, Cohn, Ferris, Glovsky and Popeo, P.C.,
signing singly, with full power of substitution, the undersigned's true and
lawful attorney-in-fact to:

            (1)    execute for and on behalf of the undersigned, forms and
                   authentication documents for EDGAR Filing Access;

            (2)    do and perform any and all acts for and on behalf of the
                   undersigned which may be necessary or desirable to complete
                   and execute any such forms and authentication documents;

            (3)    execute for and on behalf of the undersigned, in the
                   undersigned's capacity as an officer, director and/or 10%
                   shareholder of the Company, Forms 3, 4 and 5 in accordance
                   with Section 16(a) of the Securities Exchange Act of 1934 and
                   the rules thereunder;

            (4)    do and perform any and all acts for and on behalf of the
                   undersigned which may be necessary or desirable to complete
                   and execute any such Form 3, 4 or 5 and timely file such form
                   with the United States Securities and Exchange Commission and
                   any stock exchange or similar authority; and

            (5)    take any other action of any type whatsoever in connection
                   with the foregoing which, in the opinion of such attorney-in-
                   fact, may be of benefit to, in the best interest of, or
                   legally required by, the undersigned, it being understood
                   that the documents executed by such attorney-in-fact, on
                   behalf of the undersigned pursuant to this Power of Attorney,
                   shall be in such form and shall contain such terms and
                   conditions as such attorney-in-fact may approve in such
                   attorney-in-fact's discretion.

       The undersigned hereby grants to each such attorney-in-fact full power
and authority to do and perform any and every act and thing whatsoever
requisite, necessary, or proper to be done in the exercise of any of the rights
and powers herein granted, as fully to all intents and purposes as the
undersigned might or could do if personally present, with full power of
substitution or revocation, hereby ratifying and confirming all that such
attorney-in-fact, or such attorney-in-fact's substitute or substitutes, shall
lawfully do or cause to be done by virtue of this power of attorney and the
rights and powers herein granted.  The undersigned acknowledges that the
foregoing attorneys-in-fact, in serving in such capacity at the request of the
undersigned, is not assuming, nor is the Company assuming, any of the
undersigned's responsibilities to comply with Section 16 of the Securities
Exchange Act of 1934.

       This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4 and 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorneys-in-fact.

       IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed this 2nd day of March, 2022.


                                  /s/ Gabriela Gruia
                                  ----------------------------------
                                  Gabriela Gruia