Rather than vent here, why not call the hotel and ask them?
Transient taxes are quite common. Get used to them.
I'm wrestling with Florida's Sales and Use Tax on short-term (< six months) rentals, which is the same thing with a different label. The rates are nothing like you're seeing but the registration and payment processes are outrageous. Among other things, I have to file every month whether I had a rental or not. Seeing as I might have maybe two rentals per year max, the aggravation outweighs any benefit derived from renting. (I rented one week in Cocoa Beach back in April, probably my last Florida rental for the year.) Also, each county has its own tax rate on top of the state's 5%.
Fortunately, if I go through a rental agent or if the resort itself does the rental, they do the filing and paying. This explains some of what EH retains on the rentals I gave them.