Maybe isopropyl alcohol on a rag first, to remove the heaviest accumulation. Don't use too much and DON'T pour the alcohol directly onto the leather - that'd be overkill and might even cause the adhesive holding the leather to the block to let go.
You'd still need to remove the embedded grit after that, if going to a finer grit compound. To do that, I'd lightly sand the surface. Some 100-150 grit garnet sandpaper (the type intended for wood) works very well for that. Wrap the sandpaper over a block of wood and sand with a light touch. Doesn't take much to remove the contaminated layer from the surface and expose clean leather underneath. And any of the relatively coarse grit of the sandpaper is least likely to remain unnoticed on the leather and won't imbed itself either. Clean it up with a vacuum cleaner and then apply your new compound. I'd avoid using aluminum oxide or SiC sandpaper, because that grit is much harder and more likely to leave unwanted scratches on your bevels, if any of it imbeds in the leather. The garnet grit is less of a scratching threat to steel, in that regard.
You might test the sanding method on a piece of scrap vegetable-tanned leather first, to get a sense of how it'll work. It's very easy and works very quickly. The leather will take on a velvety nap after sanding. But applying new paste and using the strop afterward will compress the nap and smooth it out again in a relatively short time.