Yes, the steel of the screws is harder than the alloy of the sliding string puller.
The solution I've done on 3 hohner Jack basses now is helicoil the string puller and all is good again.
I have done this for nothing for someone on here, but if the thread on the proper Steinberger screws isn't metric (m4 iirc) I don't have the kit for doing it.
You could try taking all the screws out and really cleaning them and reassemble with a good grease like copper slip.
If you've lost too much material from the puller bit,eventually the thread will slip.
Try the grease thing first but if you can verify the threads are metric I can helicoil them for you.
Cheers
MBA