How to get rust off punched tin?

I have a very old hutch my grandfather's brother built. I'm guessing in the '30s. I have refinished all but the upper half. The 4 doors (2 upper & 2 lower) are made with each door inset panels of punched tin. They all have rust on them. I have scrubbed but can't get then clean. Don't want to take them out. It would just take away from the piece. Any suggestions on removing rust? Thanks for any suggestions!

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