Denatured alcohol (paint/hardware dept.) will remove Sharpie and other inks from most surfaces (haven't found one it won't work on yet). Put it in a spray or squeeze bottle, spritz it on the mark (it doesn't take much) and wipe off. Repeat if necessary.
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I use it a lot at work and have gotten it on me with no weakened or fade-out spots on my jeans, scrubs, or work towel. These have been washed 100+ times so I would definitely test it on color-fast materials or carpet first to make sure.
It will also dry moisture quickly. I use it in my shower and on my windows before I put on suction cups or stickers and will also help in the removal of the glue that stickers leave behind.