What brand are you using? Black or white?
I don't have too much trouble with this - only if I leave the tape in the thumbhole, in the car, on really hot days.
Try some "tape residue remover" pads - your pro shop should have them. Once you get all the crud out of the thumbhole, this problem might stop.
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Ability is what you're capable of doing.
Motivation determines what you do.
Attitude determines how well you do it.
- Lou Holtz