Specifically catalyzes the dephosphorylation of 2-phosphoglycolate. Is involved in the dissimilation of the intracellular 2-phosphoglycolate formed during the DNA repair of 3'-phosphoglycolate ends, a major class of DNA lesions induced by oxidative stress (By similarity). 2-phosphoglycolate + H2O = glycolate + phosphate Organic acid metabolism; glycolate biosynthesis; glycolate from 2-phosphoglycolate: step 1/1. Belongs to the HAD-like hydrolase superfamily. CbbY/CbbZ/Gph/YieH family.