In what way is it dirty? If its got stains they may be from the glue or from mould if there is water trapped under it.
If it's been used by a smoker before that will make it quite yucky. Best bet may be to find a cleaner one in a scrap yard, or try a dry foam carpet cleaner with a stiff brush.
Wouldn't go charging in with a stiff brush unless you have no other alternative.
Roof cloths are notoriously fragile and scrubbing can damage them very quickly.