The cat was an improvised thing. Brando is infamous for his improvisations. Like in On the Waterfront, when Eva Marie Saint drops her glove by accident. Brando could have just picked it up and given it back, but he used it as a prop. He sits on the swing, fidgets with it, even goes so far as to put the glove on his own hand. None of that was in the script. Same with the cat. It's also kinda sinister and creepy too, how they're discussing murder, and he's just sitting there stroking a cat. FFC was throwing a fit though because the cat's purring was drowning out all the other noise.