I have noticed this on mine in the past and I have used Meguiars ultimate paste wax to restore the trim. There are probably many other products that have more cutting action, but the Meguiars is very safe. I restored my Gibson headstock with this wax where all others failed and it is a great product, if expensive! (Link below to where I purchased it).
https://www.amazon.co.uk/Meguiars-G1.../dp/B004HCS4PK