I'm not sure you can clean it up - the abrasive particles are really tiny (micron sized) and it doesn't take all that many to keep abrading the steel. I think it's best to just leave the strop as it is and get a new one.
Short term you can strop your razor on newspaper (on flat surface) - it'll work well enough, though leather afterwards would improve it a bit. Again, this is just temporary until you are able to meet with Kelly, it's really hard to troubleshoot things like these over the internet, so our advise could be wrong just because we can't see your gear in person, inspect it, test it - see what the issues may be and how to fix it. So I'd err on the 'don't do stuff that could cause more damage' side.