I never hear anyone use cut price in place of low price or discount price.
So, probably no searches for it.
It's mildly brandable.
Three words takes away from brandablilty.
To me, it's $RegFee. (sorry)
Have you noticed CutPriceHotels.com? They claim a TM on the logo in the header there. Maybe they will have interest? For just the name, I personally think you're right around the reg fee - maybe you can off it for low $xx to someone in the Bargain Bin area if you're looking to get rid. Best of luck.