Remove it completely. It’s a hack job. I’d get a piece of 3-4 inch wide, flat molding from the big box home store and secure that across the bottom, with the ends going out an inch or so past the window trim, then paint to match.

I'd also check that exterior for any leak based on the condition of that drywall seam.

That's a window stool. The more you spend, the nicer it will look.

A new stool apron is all it needs, proper dimensions of course. Very cheap to do and moderate carpentry skills needed.