i'd be inclined to think some damp steel wool would do the trick. if the dye is really stubborn then i'd try either liquid hand soap or laundry powder to assist. laundry powder just with a litle water into a paste or liquid soap on its own with no water. both of those things help me clean brushes ive accidently not rinsed covered in water colour or acrylic paint, so i imagine they'd work here.

i can't be 100% sure this will work for the exact dye you've used, so maybe wait and see what others say, but if i was in this situation that's what i'd try.