Some forget that the black that builds up is oxidized steel
and it also has abrasive and polishing qualities, qualities that I like.

Black dyed leather hides this good stuff...

I like to occasionally scrub a strop with dry heavy brown paper
or newsprint. Color some heavy brown paper green and scrub that
green onto the strop -- good sand paper does not release grit like
woodworking flint paper but make sure you do not transfer
grit to the strop by accident. Leather tolerates a lot some so long term
it all works out.