How to cover/repair this piece of the bath tub

I recently took apart the bathroom in my basement. It was a steel tub and I had to bust up the tiles around it to take the screws out, then bust a hole in the other side of the wall to disconnect the plumbing. If you don't need to save it, take your anger out on it. Just be careful not to smash it near the plumbing and be careful to smash it only where it's not directly contacting a stud. If you hit it wrong, you could damage the other side of the wall. I would get everything around it down to bare studs before trying to remove it, just to be safe so you can see what you're doing.

Also, some bath tubs have their base set in thinset. If that's the case, you'll probably need to cut a section of floor board out and replace it.

This is a discontinued brand/manufacturer called Valley. My faucet handle broke and I saw your picture while I was researching for a replacement. I was able to get a replacement today from Biard & Crockett Plumbing Service Inc in Orange, CA.