The CC merchant agreements used to prohibit charging the customer for the charges.
Friend of mine that worked at a bank had a furniture store try to do that, she got hold of some muckity-muck at the CC company while the salesperson watched (after warning them that this wasn't how any of that worked), the furniture store had their credit card machines suspended before she left the building. There was copious wailing and gnashing of teeth that she watched with a smile. She refused their offers of a heavy discount to make a phone call again and walked out.
They removed that part a couple years ago from many of the merchant agreements.