I had this problem in Tryp hotel in Madrid.
By default, their mchine bills US cards in USD under awfull exchange rate ( 1.25 vs 1.2 at the market that day).
I refused to sign and they reversed charge.
Then they called bank and bank explained them how to instruct machine (enter some key combo) to charge in EUR.
They have done so - but my original card started declining (later on figured out that the first transaction was not canceled but revesred - so first authorization stayed). Good that I had a backup card which I had to use - albeit not a reward one.
So, my total loss was about $10 - lost opportunity on the reward