The simple answer is no, they can’t force you to use a wrapping service, but at the same time
they have the right to refuse a bag. I would ask for a red coat or supervisor and ask why the bag is being refused as-is when the mistake was corrected.

Had a similar agent in TLH on a power trip a few months back that insisted a properly locked gun case needed one more lock. The agent “sold” my father one for $20 and he applied it to avoid missing his flight. Definitely not a service DL provides and was a rogue agent. They are out there.