Cleaves the gamma-glutamyl bond of periplasmic glutathione (gamma-Glu-Cys-Gly), glutathione conjugates, and other gamma-glutamyl compounds. The metabolism of glutathione releases free glutamate and the dipeptide cysteinyl-glycine, which is hydrolyzed to cysteine and glycine by dipeptidases; it may function in amino acid uptake/salvage, or possibly in peptidoglycan linkage. Catalyzes the hydrolysis and transpeptidation of many gamma-glutamyl compounds (including some D-gamma-glutamyl substrates), with a preference for basic and aromatic amino acids as acceptors. The KM values for gamma-glutamyl acceptors are so high that it has been proposed transpeptidation is not the physiological role in E.coli