removing paste from a strop

I have Thierrs-Issard paste on the linnen side of one of my strops.It soon became rather black from the metal removal.Is there some way/need of cleaning this up?

No, I don't think there is. The black is the effect of the paste cleaning rust and metal off you're blade.
This said just because it is black doesn't mean that it isn't still doing a good job.

I know it's to late to tell you, but it is best to keep a clean strop and a dirty strop.
You now have a dirty strop and need to get a new one if you want a clean strop.

Clean strops only stay clean if you ensure the blade is spotless.

One of the problems with pastes is that they are dirty. One of the problems with leather is that it will wax up and take on a black sheen if the blade is rusty or dirty or has paste deposits on it.

You can clean the leather by scraping it with a sharp edge or rubbing it with a pumice stone or using a cleaner on it. But linen is basically a rough cotton and getting filth out of a thick shirt is as you know, not so easy.

ok, I actually have my doble tony miller heirloom thats not to be touched by any paste or the likes.
The paste is on my first strop, that I don't use for anything else.I don't really see the need for the linnen side, so I used it for paste.Do you think paste work better on leather?

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.