I know that a white technical eraser ( like Staedtler). was recommended to me to get marks off my white leather jacket. By Danier, who would know. Don’t know if that works for dye, but it can’t hurt.
I got navy dye that transferred from a denim jacket onto a white linen top earlier this year, in the armpits. This is what I did (found the idea online):
Made a solution with 1 tablespoon of vinegar, 1 tablespoon of dish detergent, and 2 cups warm water. I used a white cloth and dabbed the solution on the stain, and blotted it with a dry cloth over and over. It got lighter and lighter. Then I figured what the heck, and stuck the whole top part of the top in the bowl and let it soak for a while. Then a wash in cold water, and voila!