Well I look at my bill to make sure it's accurate.
But when I'm overseas it usually shows at check-out the local rate (which w/ my travel patterns is normally GPB or Euro) - ie, 55GPB. I look at that & go ok that matches. Then when the cc bill comes & the US amount is shown I go fine, that must have been what the exchange rate + the cc fee turned out to be.
I don't think it ever occurred to me to try & figure out what the exchange rate was at the time of booking & check-out to see if they were the same or something like that. It is what it is, and is obviously beyond my feeble (now champagne-induced) mind.
I get reimbursed by clients for overseas travel, so whatever it comes out to in $$ on cc is what they're charged. But in fairness that's the same for me for personal travel too.
PS - if the hotel is just putting the charge through to the cc, isn't it the cc that 'plays around' w/ the exchange rate & not the hotel? And I thought most cc's checked the bank daily rate.