The problem for OP is not what could be justified. It's ensuring that OP doesn't create a conflict of interest, or a perception of conflict of interest.

You have to assume that anyone else who sees this transaction might think your points are junk, and you are being opportunistic to finally find a way to use them somewhere, and now you want your employer to pay you for it.

If your office needed a new coffeemaker, and a coworker had just coincidentally got a free $50 coffeemaker as a gift, would you expect the company to pay them $50? It might be a good deal for all, but you have to expect someone might say "wait a minute".

This sounds like way too much risk and potential hassle for little reward.