That Which Belongs to Itt

A nice counter balance to the Berkeley tree sitters and Code Pink is hearing an hour long discussion on a local station with a grammarian and a heated debate about its vs. it's and the confusing logic behind the two. What hasn't been brought up though is how one would deal with this in the case of Cousin Itt. To my mind, it would be correct to say, "We went to the opera in It'ts car."

Not directly related, but when as a child and heard the Beatles singing "Itt's drivin' me mad, Itt's drivn' me mad, Itt's drivin' me mad..." I thought they were referring to Cousin Itt. Of course, I also mistook "Woman, have you got cheating on your mind?" as "Woman, have you got chili on your mouth?"