Brain and Tufty have been enemies ever since Tufty "insulted" Brain. They had no other interactions in A Cased Suit.
Episodes Suggesting a ConflictEdit
In Wiping Off, after Brain says everyone is stupid, Tufty "insults" him and asks him how he will get down. He jumps and survives by wat presumably is Wandy's spell. Later, during the challenge, Brain kicks Tufty off the platform, saying that that is what he gets for insulting him.