scrape out the tuner holes as best you can.
bunch up some t shirt material, or thick cloth like and old face washer and wrap it around your finger.
soak it in water.
rub /scrub the area you don't want timbermate on... rotate the cloth and keep it pretty wet, you should be able to get pretty much all of it off.
remember that any water running back through the tuner holes will affect it on the other side, but let it dry and simply re apply