Yes, there is a grease fitting tool. It looks like a plus sign. It has a tap, easy out, and 2 "sockets" for different size grease fittings. Put the easy out side into the broken grease fitting and hammer on the tap end to tighten it, then grab it with a pair of pliers and remove the broken piece. Go into a good auto parts store and ask for a grease fitting tool. I know Lincoln makes a good one. Good luck.
Andy