How about CLR - Calcium, Lime, and Rust remover.
If I recall my chemistry correctly, you want some liquid which is acidic in nature a Ph of 7 or much less is better. This will dissolve the metal/rust etc.. Hopefully, the rings causing the problem will dissolve before the other metals .... Cheap white vinegar, maybe drain o, lime, etc dissolves metals/rust. Ask someone in a hardware store, they might know a better solution .... It must sit for a couple of days for the chemical reaction to work, and maybe you will have to repeat the process. Any oil is not acidic.
