Years ago they used to sell a "suede sponge"....I suspect it was very like a Magic Eraser....try it on something else that's suede...I expect it will do the job.
But....another thought....the stain may be oil from your hands....and brushing it gently with a soft toothbrush and corn starch or corn meal may well remove the oil....and it's a pretty no-harm thing to try first. Rub the corn starch into the spot, let it sit for a few minutes and then brush it off ...you may need to end up with a vacuum to get all the white out....and of course, keep everything dry while you are doing it.
Linda C

Thanks, Lindac. I'll give it a try.