There's nothing that will permanently remove the ink used in those markers, once its dyed fabric, either natural or manufactured from cellulose or petroleum byproducts.
I recently came across over 100 brand new NOS Pattern 37 broad arrow C marked slings.
Somewhere along the way, a brilliant entrepreneur decided to mark each of them with $1 with a black marker. I tried everything from Varsol, to Acetone to Gasoline and even a mild Muriatic Acid bath. Nothing would remove that ink. Barely faded it.
I ended up selling them all to a friend who will be using them for "handles" like those seen on transport chests.
Too bad, because they were otherwise perfect.