Paste is normally applied to a leather strop not linen. They do sell some paste for linen but its not abrasive.

Once you apply paste to leather you should consider it a permanent decision. I have heard of guys using some soaps and degreasers to clean paste off however paste is abrasive and some will embed itself in a strop and never come off. You could use a pumice stone but to rub hard enough to get it all off will probably damage the strop.