
I would remove the bed and just give him a piece of vet bed to lie on or a cotton doormat like mien like to use in the daytime in the kitchen. I am assuming he doesn't pee on the tea towels when he pulls them down.
I suspect it may be that the bed has become impregnated with a small attracting him to pee on it, or even the cleaner smell is unpleasant (if it has ammonia in that would smell like another dog has peed on it, so he would want to cover it up) and he wants his own smell on it, and it is now a habit, take it away ans you break the habit.