First, if the handle is simply soiled from use, then warm water and mild dish detergent will do wonders.
If it's roughed-up, then after cleaning via the above, use some 400 to 600 grit sand paper, going with the grain of the cork, not length-wise.
If there are hook gouges or small holes, then mix some cork dust with either Elmer's or Titebond II or III glue, apply, and let it dry for at least 24 hours or even longer. Then sand with the same grit paper as above.
Send me a note or message if it's worse than that. I make cork handles from scratch for bamboo rod restoration when necessary and have cleaned and/or repaired quite a few originals that were anywhere from 100 to 40 years old.
I usually don't bother cleaning cork unless I want to sell a rod on ebay and want it to look nice in the pics. When I do I use warm water and baking soda and scrub lightly with the rough side of a dish sponge.
Before I use the rod, or after I've cleaned it up a bit... put's a light, brownish varnish tint at first, but that wears down. makes cleaning up a soiled rod a lot easier, and does a good job of protecting from light chips, etc.
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