My experience is once a strop is pasted it's contaminated for all eternity. Removing pastes is not easy especially when dealing with microscopic particles. Your best bet is to get yourself a dedicated unpasted strop and keep it that way.

I've had a few pasted strops that I've tried to unpaste. I used pumice and lather and neatsfoot and when all was said and done they still cut. I'm not a big fan of continually stropping with a cutting paste. It wears away the teeth instead of polishing them and thus reduces the life and usefulness of the edge. Their will also be a rounding effect on the edge over time and the bevel will need to be reset.

My 2 cents for what it's worth.

Regards,
EL