Moisten a rag with oil. Try any cooking oil, moisturizing lotion or lubricating oil. Heat the oil in the microwave before moistening the rag to increase its effectiveness.
Daub the oil onto the surface of the tape to saturate the surface and edges of the tape. Do not add so much that the oil drips freely down the wall. Leave the oil to sit for 20 minutes.
Scrape the double-sided tape off the wall with a plastic putty knife. Hold the blade of the putty knife at roughly a 30 degree angle to the wall. Start at one end of the carpet adhesive and push forward with short, firm strokes. Take care not to gouge the wall. If you can lift one edge of the strip, try pulling the entire strip up with your fingers. If you hit a few stubborn spots, don't force the tape. Cut away the carpet tape you've removed so far, then reapply the oil and try again.
Mix a mild soap solution with 1 teaspoon liquid detergent soap and 1 quart of water. Dip a clean sponge in, wring it out and wipe the wall free of any oil residue.
Dip a clean sponge in fresh water, wring it out and wipe away the soap solution.
Wipe the spot with a clean towel.