I removed all the solder as Neil suggests. But to pull the solder out with the wick you may need to add some a little solder to the top of the hole first so that you get good thermal conductivity between the wick and the solder you are trying to remove from the small hole.

Are these really Phillips 00 screws? My supposedly 00 screwdriver is way too big. Maybe they are really Phillips 000. The screws in my device were set with blue locktight (grr). I was able to unscrew three of the six with very small straight edge screwdriver but had to sand off the heads of three more with a Dremel tool. This is dangerous. During the process I barely nicked a component near where the antenna cable connects to the logic board. Now I have a new battery and no WiFi.