Removing caulk from "caulk strip"

In Arizona, when we moved into our home, we made the error of using the pre-caulked rubber stripping to seal around medicine cabinets and the vanity cabinets. These strips have since succumbed to gravity and slipped down, leaving a caulk residue on the painted wall and wood cabinets. The sliding rubber pulls off easily enough, but what is the easiest way to remove the sticking removing caulk? I am not worried about ruining the paint on the wall, but I am a bit concerned about the finish on the oak vanity cabinets. Thanks
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Anyone have any suggestions? Thanks

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