This was the path I pursued when I did not get satisfaction from Hilton or the 3rd party. At first, the credit card company (Discover) did issue a credit. They reversed that decision two weeks later. I had several back and forths with them after that. I sent emails that illustrated the window of cancellation for refund, and when the cancellation was sent. I also sent emails, and phone logs showing my attempts to contact the 3rd party, along with those to Hilton. I asked for an explanation as to why they reversed the decision and not honor my request to decline the charge, but I never got an answer.
In the end, big business sided with big business to the surprise of no one. As a result of that, I also paid off the balance on that card and froze the account. So in the end, two companies lost my business because of a $250 refund that absolutely should have happened. And even though I'd never had an issue in the past, I am also far less inclined to book through 3rd parties now even though they offer a discount. I'd rather pay more and work directly. The amount of time and effort spent fighting this was definitely not worth the savings.
As a retired business owner, I always strove to put my customers first. If I chose a contractor who failed to deliver on their obligations, that's on me. I chose to get in bed with that contractor, not my customer, and I clearly made an honest but poor decision. But my business was not enshittified. I wasn't beholden to shareholders or private equity, who's money is made in the margins of declining levels in service, satisfaction, and quality.