De-soldering Through-Hole Solder
There might be no pad left on some of those pins, looking at the pics. That said, a combination of these will work:
A solder sucker - terrible name but yeah, thats what it does. Make sure to get the silicone tip so that you get good vacuum between the tool and PCB. If you haven't successfully removed the solder, you might want to add more solder to &quot;close&quot; the pad so that the vacuum will work better on the next attempt.

Desoldering wick. It will draw the solder via capillary effect. Use plenty of flux and DON'T rub the pads.

For larger connectors, preheat or hot air might also help.