Magic eraser will destroy it. My wife had a a pink Chanel (different style, but same idea) nd it had blue dye from blue jeans which rubbed against hers.
I bought some good saddle soap (it is really great for all things leather, I would go with
coach, allen edmonds, or Fiebing's on
amazon) and went to town on it. I keep some soft toothbrushes around and scrubbed and scrubbed, reapplying soap every 3-5 minutes. After about 45 minutes, the bag was as good as new. Actually, it seems to pull off so much of the moisture that is naturally in leather, afterwards I had to get leather lotion (Coach or Allen Edmonds make great ones) and applied it about 4 times. That part took about 10 minutes. The bag looked better than new and felt as soft as belting butter.
Good luck