The son of Van Dyke’s bank chairman (the next morning when they were flying kites) told Mr. Banks his father died laughing after he pondered the joke Banks’ told him about a man with a wooden leg named Smith (when Banks was fired after being summoned at night to the board). Since it bumped the son up to chairman, he was able to rehire Banks, and with a promotion (although baffling why he’d hire the man who “killed” his father - but it was a fantasy, after all).
Of course, as was pointed out, P.L. Travers hated the original film, felt Uncle Walt screwed her over, and so much so that she refused to allow any very lucrative sequels at the time. I’m amazed they were able to make this one, as she was adamant about no sequel films (she lived to 1996 just to make sure they wouldn’t).