Mr. Clean magic eraser. And I would advise taking an extra english class.
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Magic Erasers are GREAT, but do rub the marks GENTLY because the eraser might erase your paint as well! Usually they won't take away the paint but can leave a lightly sanded look to glossy finishes. And another warning here about Magic Eraser sponges: THEY ARE HIGHLY ADDICTIVE! :) You'll be scrubbing floors, tile, outside toys and furniture, inside of aquariums, stoves, inside of fridge (I won't clean a fridge without a Magic Eraser anymore), upholstery in your car....etc, etc, etc You'll become hooked - I promise! My daughter says I should be their spokesperson! :D
Try wood alcohol (I used it to get sharpie off a fridge, a whiteboard and a window)
You can get wood alcohol at auto parts stores or truck stops, it's sold as air break antifreeze for trucks.
plain ol' rubbing alcohol will act as a fine solvent for that type of ink, too
if its permenant marker - use a WHITEBOARD marker (dry-erase) and rub the markings. Dry erase wont come off either, but it will dissolve permanent ink. Then use white-board cleaner to remove the dry erase.
I wouldn't recommend goof-off, because it might dissolve and melt the marker into the fridge enamel. I had to do this before - worked like a charm. Also try mr clean magic erasers.
There's a solvent called Goof Off that I'd try
Bleach or hydrogen peroxide might 'bleach' the marker-ink so that it is less/in-visible. Try this on a bit of the fridge that is usually hidden from view first, to check that it doesn't have an adverse effect on the textured finish.