Cat's Pajamas is a side-mission in Marvel's Spider-Man: Miles Morales. This side-mission will unlock, once you completed Looters!!! side-mission and finish the main story.
This mission is short and easy; just visit Ted's Grocery in Harlem. As you walk in to the store, the store owner Teo will greet you and how he told everyone that he saved Spider-Man.
Just press to pet his pet cat Spider-Man. Once you do that, Teo will give you a new suit.