Séchoir à rouille rétractable en accordéon antirouille

I have this in a shower to hang washcloths to dry and swim suits. Unfortunately it has rusted and I cannot figure out how to remove the rust permanently.

So far, so good. Perfect size - a bit deceiving at first with the telescopic rungs. Looked too short at first. Looks strong enough to hold several small hand towels and some shirts on hangers over our utility (dog washing) sink.