To clean the pump, prime and activate the pump a few times. This pushes a rod through the nozzle and ensures that solder doesn't block it.

On the rare occasion when the pump needs a more thorough cleaning, you can disassemble the pump to clean it out:

Grasp the nozzle by its knurled edge.

Twist the nozzle counter-clockwise to unscrew it. This may be difficult due to a tight-fitting O-ring.

Remove the nozzle and clean out the pump interior.