Protease that acts as a positive regulator of the cGAS-STING pathway by catalyzing desumoylation of CGAS. Desumoylation of CGAS promotes DNA-binding activity of CGAS, subsequent oligomerization and activation (By similarity). Deconjugates SUMO2 and SUMO3 from targeted proteins, but not SUMO1 (PubMed:18799455). Catalyzes the deconjugation of poly-SUMO2 and poly-SUMO3 chains (PubMed:18799455). Has very low efficiency in processing full-length SUMO proteins to their mature forms (PubMed:18799455). {ECO:0000250|UniProtKB:Q8BUH8, ECO:0000269|PubMed:18799455}. This is the function of SENP7 (SUMO specific peptidase 7, ENSG00000138468).