Have you tried using non oil-based eye make up remover?
My nova check medium tote has unfortunately gotten the dye transfer from my black cardigan too. I left my bag alone for 2 weeks until I came across a thread in Purse Forum that there are members who said Dior Eye Make up Remover or Chanel Eye Make Up Remover help in lightening the dye transfer gradually.
I used Loreal gentle eye make up remover and pour a little onto a facial pad cotton and gently buff the stained area in circular motion and I could see the stain on the facial pad cotton. It will not remove the stain instantly, however it does make the stain lightens and far less obvious. I still have only a bit of dye transfer left and I'm going to try using it again
Hope this helps.