The Cat's Pyjamas mission is a mission where you head over to Teo's Bodega after completing the campaign. You can access this mission in the FNSM (Friendly Neighborhood Spider-Man) app.
After The Battle For Harlem, Miles is recovering after his mission and from Phin's death. He decides to visit Teo's Bodega and pet his cat. As a token of gratitude for rescuing Teo's cat, he lets him go along with Miles to accompany him on missions, thus earning the Bodega Cat Suit.