Conditioning a Strop with Graphite

I've been experimenting with graphite on my strops. My question is about conditioning the strop. For a clean strop, I simply rub my hand across the leather like it's recommended on this site in a number of places. For a strop with graphite, however, you end up with a black mess no matter how well you clean the strop. So the question is how does one condition a strop that's been treated with graphite? Thoughts?

Oil it on the back side. Apply conditioner to your hands and then rub the back of the strop.

Thanks. What would you do with a paddle?

You mix the Graphite (or any abrasive) with a strop conditioner

IE: On my bench-strops (basically a paddle) I mix CrOx and CeOx powder with Fromm strop conditioner as the carrier so I condition the strop with every application too...

Makes sense. Thanks.