I use a strong netting and a loofah sponge. I've just gotten a new one that is self healing and the net is all I've needed to get the little strings. The old mat had no healing properties, I wore grooves into it and had to number it backwards. I did use a really fine fine sand paper on it to get the highest edges off the grooves before I renumbered it.
I wish I could afford the really big self healing.....that would be a special treat!
Happy Quilting,
Sharon