Cleaves the gamma-glutamyl peptide bond of glutathione and glutathione-S-conjugate such as leukotriene C4 (PubMed:21447318). Does not cleaves gamma-glutamyl compounds such as gamma-glutamyl leucine (PubMed:21447318). May also catalyze a transpeptidation reaction in addition to the hydrolysis reaction, transferring the gamma-glutamyl moiety to an acceptor amino acid to form a new gamma-glutamyl compound (PubMed:21447318). Acts as a negative regulator of geranylgeranyl glutathione bioactivity by cleaving off its gamma-glutamyl group, playing a role in adaptive immune responses (PubMed:30842656).