Hi Jed,
Another thing you can try on grubby areas is to massage in some baby Oil, let it tit for a few mins then scrape over the area (light pressure) with the a blunt straight edge, like the eds of a bank/store card or the back edge of a butter knife. Just make sure the edge is not as all sharp!
Once you've got the muck off, pat the area dry with a towel and apply baby powder of cornflower.
If its a Stain from clothing, that another thing entirely and will need one of various methods to try to lift it out.
K