Catalyzes the conversion of hemimercaptal, formed from methylglyoxal and glutathione, to S-lactoylglutathione (PubMed:20454679, PubMed:23122816, PubMed:9705294). Involved in the regulation of TNF-induced transcriptional activity of NF-kappa-B (PubMed:19199007). Required for normal osteoclastogenesis (By similarity). {ECO:0000250|UniProtKB:Q9CPU0, ECO:0000269|PubMed:19199007, ECO:0000269|PubMed:20454679, ECO:0000269|PubMed:23122816, ECO:0000269|PubMed:9705294}. This is the function of ENSG00000124767 (GLO1, glyoxalase I).