Skip the Harsh Cleaners: You Can Remove Rust with a Potato! The potato trick is so handy (and non-toxic!) and it isn't limited to cast iron — you can use it to remove rust from baking pans, knives, and other household tools. Tips from The Kitchn
Evaporate trapped moisture (the cause of the stain) by directing heat at it. Start with the blow dryer on the low setting, so as not to burn the wood; if that doesn't work, turn the heat up. Get the tutorial at Homemade Mamas.