All accounts I’ve found say that her producer, Rick Chertoff, had heard the song on Hazard’s EP. This article confirms that the song was on the EP. Here’s another article that says that Hazard and the Hooters were college buddies and that Chertoff, an old friend, was very familiar with the song.
The first answer on this Quora page has some insights into the changes Lauper made.
I’ve always found it interesting that “Money Changes Everything” (which I like a lot more than “Girls Just Want to Have Fun”) was written by a man (Tom Gray of Brains). The lyrics don’t really suggest either (or any) gender, but it just surprised me when I learned this. His (Brain’s) recorded version is actually quite good.
The boys watch the girls while the girls watch the boys who watch the girls go by.