Contributes to degradation of proteins cross-linked by transglutaminases. Degrades the cross-link between a lysine and a glutamic acid residue from two proteins that have been cross-linked by transglutaminases. Catalyzes the formation of 5-oxoproline from L-gamma-glutamyl-L-epsilon-lysine. Inactive with L-gamma-glutamyl-alpha-amino acid substrates such as L-gamma-glutamyl-L-alpha-cysteine and L-gamma-glutamyl-L-alpha-alanine.