Metallocarboxypeptidase that mediates tubulin deglutamylation. Specifically catalyzes the deglutamylation of the branching point glutamate side chains generated by post-translational glutamylation in proteins such as tubulins. In contrast, it is not able to act as a long-chain deglutamylase that shortens long polyglutamate chains, a process catalyzed by AGTPBP1/ CCP1, AGBL1/CCP4 and AGBL4/CCP6.