Folks above gave plenty of thoughts on how to clean the rust on this, allow me to chip in with a suggestion to help prevent it recurring.
Camellia oil can be thinly applied to exposed metals like this, it will inhibit the rust formation, and better yet, it's woodwork safe, insofar as it won't then cause too many issues if it gets on your work.
Please note camellia oil for woodworking is a different product than camellia oil used in the kitchen, they each have separate additives to help them do their respective jobs.