Anyone ever had this happen, and what can be done?

Basic story is this: checked in for an international long haul at the airport desk since it was easier - needed a bag checked through on a separate reservation. That part worked.

After clearing security, went into the reservation to check which card was being used for in flight purchases. Noticed it was a Chase Visa from my profile, not an Amex which I typically use, since I get reimbursed for that. Go through the steps and confirm the change. During flight, I purchase an alcoholic beverage and seems to be ok. Until a couple of days after flight, when I get the receipt and notice it is being charged to the Visa, instead of the Amex I specifically changed it to.

Use messaging to reach out to UA, let them know the issue, and that the charge needs to be switched to a different card. They claim it can’t be done, and that I need to talk to refunds to sort it out. So I put in a refund request, but pretty sure that’ll be denied. To be fair, I did authorize a purchase, but not ok is that it was done to the incorrect card, and there should be no authorization as it was confirmed as switched to the new card.

I realize I’ll have to wait for refunds to get back before I do anything else, but wondering if anyone has had this happen before, and what my next steps should be. Like I said, I have a feeling the refund is going to be denied, so looking at how to get this sorted amicably. For me, $10 to wrong card is not the end of the world, and if it was my mistake to choose the wrong card, that’s on me and have no problem taking that responsibility. But I don’t think UA should be able to choose which card gets charged, especially when I specifically authorized a different one.