I’d never heard of a pelmet either, but when I searched for images of a pelmet all the websites came up "uk". So maybe this is one of those Britishisms. All of the pictures that came up were of, what I would call, a valance either soft of solid (cornice).
Scroll down past the Roman Blinds and Cut-Away Pinch Pleats to the Double Diamond Pelmet. In American English I would call that a topper or a valance.
They also call this a pelmet, but I would call it a cornice board or just a cornice.
I found this while surfing that describes a cornice, but scroll to the bottom of the page and it shows a cornice draped with a pelmet. I would have still called this a cornice.
Now get out your pens and paper for the pop quiz at the end of the drapery lesson for today . . .
The neighbors said that they knew the man who'd been shot for years.