I've discovered that using Crest's 'Whitening Expressions Fresh Citrus Breeze Liquid Gel' toothpaste removes black permanent marker from the textured surface of a white refrigerator.
Just dampen a sponge and put a small amount on the corner and gently scrub away. It will take some patience.
I didn't use very much pressure as I was afraid of dulling the surface. It came out looking like new.