I thought it was just a table gift from AD. It IS a Gene hat, not a Barbie hat. It’s a 1940 style called a “doll hat”. It perches forward on the head and the ribbons are tied in back, behind an updo. I’m trying to find a photo to show.
Dorothy: Who’s that? Scarecrow: A strange man with an axe and a can of lube. I’ll ask if he wants to join us?