The through holes must be cleared of any leftover solder.

Place the hot iron on the side of the through hole with the most solder, and the desoldering pump on the other. Once the solder liquefies, press the trigger of the pump to clear the through hole.

If you're having trouble with removing solder, it is helpful to use flux dispensing and flux removing pens. Additionally, switching which side the hot iron and the desoldering pump is on helps.