Do you mean the silk? I have small grooves in the whateveryouwannacallitifyoucaretocallitanything strip at the top of my one year old tailpiece and it doesn't bother me at all.
If the felt on the ball end behind the tailpiece were missing I suppose the balls would be grooving the back of the tailpiece.
We wouldn't want to have that now. Behave yourself.
Edit: I couldn't figure out how to work a 'felt' in there. Sorry.