Catalyzes the cleavage of glutathione into 5-oxo-L-proline and a Cys-Gly dipeptide (PubMed:27913623). Acts specifically on glutathione, but not on other gamma-glutamyl peptides (By similarity). glutathione = 5-oxo-L-proline + L-cysteinylglycine kcat is 7.6 min(-1) for glutathione. Monomer. Belongs to the gamma-glutamylcyclotransferase family. ChaC subfamily.