Bar Keepers Friend is a rust remover. I used it very successfully when many years ago, I had an old washing machine that had chips in the tub and if I let the clothes sit too long, they would pick up rust from the chipped metal drum.
Sprinkle it on, and take a soft toothbrush with a little bit of water. It takes it right out. Be sure to rinse well.
Good luck and let us know what happens.