Molars and premolars normally cannot be removed, due to their strong fork like roots, the jaw bone can crack with attempt to do so. Sometimes GSDs have these teeth missing, and with the preliminary checks for the dog show it is discovered. These dogs' owners try to lie, saying that the tooth was removed by the vet. But nobody can fool the expert, who knows that it is vertually impossible to remove a molar without damaging the jaw! Crushing the tooth and extracting it fragment after fragment has its own complications, it would mean long term anaesthesia, too bad for heart despite all says about it. So, follow the advise of your vet and go for pulp removal and canal cleaning and filling. In a year time damaged tooth may start to rot at the bottom, you better come back for X-ray check if you noticed that your dog doesn't chew on that side. But then the jaw tissue would soften and it would be much easier to remove it.