You need to use a quality heavy duty soldering iron and solder wick. The pickup needs to be firmly secured to keep from sliding around when you are working on it. Don’t clamp the pickup into a metal vice as it will act like a heat sink and keep the solder from being easily removed. You need to use wood insulators if you are clamping the pickups in a vice. Use the solder wick to remove the majority of solder and do not get the pickup or joint too hot.

After the pickups cools, gently pry first by hand the inside cover walls away from the bottom plate where it is soldered. You will hear two little snaps as the solder joints break away and gently lift the bottom plate out of the cover. This works about 95% of the time for me and if you can’t break the solder joint, then gently pry on it with a plastic knife so you don’t scratch the bottom plate or bend the cover.