Gamma-glutamylcyclotransferase acting specifically on glutathione, but not on other gamma-glutamyl peptides. Allows utilization of gluthathione through subsequent cleavage of the Cys-Gly dipeptide by Cys-Gly metallodipeptidase dug1. glutathione = 5-oxo-L-proline + L-cysteinylglycine Belongs to the gamma-glutamylcyclotransferase family. ChaC subfamily.