If the tip is genuine horn, you should be able to restore the colouring buy the judicious use of metal polish. Duraglit which is a metal polish absorbed into a felt like wadding is what I have used for many years polishing Rams and Buffalo horn.

The polish removes virtually no material, it just cleans it up. It may pay to use masking tape on the adjacent woodwork whilst polishing the horn, it will stop any of the polish impregnating the wood.

Harry

Biology is the only science where multiplication can be achieved by division.