Capacitors are removed from the board using heated tweezers where possible in order to avoid damage to the pads. Where there are restrictions due to space, I would normally use a small soldering iron or very occasionally hot air. I NEVER use a pair of pliers to twist the capacitors off – despite many YouTube videos showing that as a recommended technique it almost always causes damage.
It is almost certain that there is corrosion under the capacitors and this needs to be cleaned before installing the replacements.

To prevent future leakage, I fit good quality ceramic capacitors. These don’t leak and work perfectly in the GameGear as well as being a much neater solution than installing normal electrolytic capacitors. Finally the area around the new capacitors is cleaned to remove excess flux.

The sound board is similarly fitted with replacement ceramic capacitors in place of the generally leaking electrolytics. The power board is usually in much better condition than the rest of the GameGear, but new capacitors are fitted anyway to prevent future problems.