First things first, you need to remove the little bit of solder that is holding the cover to the pickup base plate. I like to use a soldering gun and a solder sucker but anything that will safely break that connection without harming the pickup is fine.
How to remove a pickup cover
Next I give it a nice warm bath in a double boiler set up to loosen the wax that is holding it on. I have also had luck just letting it sit in a sink full of hot water.
After a few minutes the wax is softened enough to pull the cover off......
....while it is still warm take a soft cloth and wipe the residual wax off the pickup then give the plastic bobbins a buffing with a dry cloth to shine them up a bit.
FYI- to put a cover on a pickup first make sure the cover fits your pickup (no, they are not all the same). Then solder the cover to the base; one small solder connection on each side is plenty to keep it on and make the grounding connection.
Next set up a double boiler similar to like I have above but instead of water in the second (smaller) pan you will be using wax; regular paraffin works fine but a combination of paraffin and bees wax seems to be popular with a lot of pickup manufacturers.
Melt enough wax to cover the pickup and then drop the pickup in making sure the wire is hanging outside of the wax and not near the heat source. You will see some air bubbles coming out of the pickup as the wax displaces the air, after about 10 minutes or so you can remove the pickup and wipe off the excess wax with a soft, dry cloth.
Warning! Do not melt wax near an open flame including gas stoves. Use an electric skillet or electric stove and always do it in a double boiler style setup.