For reapplication after removal, I do charge but I incorporate this fee into my overall service price.
If it's a removal with no reapplication of my own product, I charge $10.
For another salons product, I do charge more as the client and myself usually have no idea what product was used and I charge $15 but if they are going to have a reapplication of my product, I only charge the $10 plus the service of application on their first visit.