The problem is that the iron reacts with tannins in the wood to create the black stain.
There is no easy way to reverse the reaction, and the chemicals to remove it (wood bleach) also affect the rest of the woods coloration.
It can be bleached out, but then you have to re-color the wood and refinish.
The usual fix is to strip the entire object, bleach it, then refinish including dye or stain to get the color back.
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