I just use a metal spatula to push the semolina and any burnt cheese or toppings off of the back of the hot steel between pies. I do a more thorough job after it cools and I pull it out. (My steel is 3/8", so not ridiculously heavy.)
I have a trick to keep the scrapings off the floor of the oven: Before I start, I put a strip of foil under the very back of the steel, leaving an inch or so exposed. I bend it up a little to form a trough, so that it collects everything I push back with the spatula.