I have this iron pan that got rusty from not being properly dried. Scrubbing it I was able to get rid of most of the rust, but there's still some I just can't remove. I thought I could chemically remove it, but I myself am a bit rusty on the inorganic chemistry subject, so I couldn't think of any way of doing it without leaving any unwanted residue on the pan.

The rust is the brownish-red type, which according to Wikipedia consists of $\ce {Fe2O3·nH2O}$ and $\ce{FeO(OH)·Fe(OH)3}$. Most rust-removal "recipes" I found involve all sorts of acids, but I can't tell what the reaction(s) would be with $\ce {Fe2O3·nH2O}$ so I can't tell if there would be any residues left behind that I could not remove. Anyone with any experience on the matter?

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I contacted the manufacturer and the pan is hand-made, just Iron and natural coating (fat).