The handle that protrudes above the back plate actually has two parts - the bonnet (the thicker, onion-shaped base) and the actual handle that moves (see a snapshot from Kohler's manual below). The bonnet threads onto the valve, so you would need a strap wrench (or strong and dry hands :) ) to turn it counter-clockwise while holding the handle down. The handle is not detachable from the bonnet - they both come out when you completely unscrew the bonnet.
This is, obviously, a reverse of the installation procedure:
formatting link
Good luck!