Do they accept cash? I have got out of paying credit card surcharges by offering to pay cash and when it turns out that the only way to pay is by card they are forced to remove the surcharge.
The last time I stayed in hotels in Australia and NZ they were also charging credit card surcharges, but they advised to pay in cash (which I am able to put on credit cards as a purchase by using Curve).
Though in the US I suppose the points earning is still worthwhile unless the surcharge is something really ridiculous.