If steel is used for the core, it can rust. No doubt about it.
To clean it off just use ink eraser as that is more abrasive than a pencil eraser. I suggest you do not use more aggressive abrasive than this for minor corrosion. In serious corrosion cases you could use a very fine 'wet & dry' abrasive paper of >1000 grit. Let the clamp peter clamp down on it and then gently pull it back and forth through the jaws. Clean the jaw faces with IPA to remove and grit and residues.
Whether the mild oxidation actually has a negative effect on the clamps performance ..... I doubt it, but have no experience of such with clamp meter designs.
Aurora