First determine what that finish might be. Call the manufacturer if the bow is current production.
If you don't know then start with the mild solvents and move toward the strong stuff. Try soap and water, then Goo-Be-Gone. Then try rubbing alcohol or mineral spirits. Think damp not sloppy wet.
If you have to go stronger, like M.E.K. or acetone, then you will most likely damage the finish.
Also, follow that wise advice on the label that says, "Try this product on a small inconspicuous area before proceeding".
Answered on 4/17/2013
The Katniss Project from Mountain Woods, NC