One way to do it is to remove the black plastic base part first. If you cut the pins flush with the plastic base it comes off a lot easier. Get one end lifted and started and it should come off pretty easily.
Once you do that the pins will just fall out when you reheat them one by one with your iron. That’s assuming you have a spare male header. Once the pins are all out clean up what solder is left with a solder sucker or flux wire wick. A wet sponge can also be used to wipe the hot solder off, if your quick enough.