Hi there...
Yesterday evening I was wondering the same thing. I applied, some time ago, some paste on a stop of mine... as a newbie mistake I pasted my best and only strop (Dovo)... I applied some strange black paste that old barbers used to touch up the razor's edge. No harm done because I made my own strops and they work fine. But I wanted to refurbish this strop because it's got a linnen side that I like and the strop is too good to be used only from time to time.
So this is what I did: I grabed a pumice stone and a piece of snad paper. With the sand paper I managed to remove some nicks and, with a light touch, remove some bits of paste that were thicker. Then I rubbed the pumice stone on the strop in a variety of circular motions. It took a while but almost all the paste came out like that... after that I cleaned the strop with a clean cloth and applied some Nivea hand Cream (the blue tub one). Did that with my fingers in a circular motion, rubbed it in and buffed up with a clean cloth.
The results were very good. The strop might add a minimal ammout of extra polish to the edge but it's not a bad thing. The strop is looking like new... Until yesterday... I was happily stropping and I nicked badly!

Managed to mend that, though... but there's a chunk missing, now!
Oh well... just my 2 cents...