Heating the case with an iOpener or the cable with a hot air gun or hair dryer will help soften the adhesive and make it easier to remove.

Peel off the button cable.

If you are planning on reusing the button / charging coil assembly, use extreme care when removing this cable. It is extremely thin and very fragile. Work slowly and carefully and put as little stress on the cable as possible.

Hold on to the cable with tweezers while lifting and sliding the spudger between the cable and the case.