Run them through a damp, not wet, clean cloth. Cleans them right up.
HOW DO YOU CLEAN YOUR CABLE JACKETS?
I've searched everywhere and there are lots of people discussing contact cleaning but no one mentions the dusty dirty jackets especially on fabric jacketed cables like Audioquest etc. I used a hand vacuum cleaner with an edge attachment, cut a radius notch in the end, then used painters tape on the edges to prevent staging the threads of the fabric. As I re install the cables, I'm considering expandable loom to protect them from dust in the future. Loom is inexpensive and disposable. Anyone else have a better idea?