You could use the solder wick method, but my preference is a Vacuum Tip
Desoldering Iron ... it is certain to clear out any solder from the board holes.
A lot of boards these days are multilayer and if you try to remove a part without
all the solder being removed, you could damage the plated through hole. You could
also clip the component off at the top of the board, then carefully remove each pin
one by one. Do not attempt to wiggle all 4 pins or so that the jack may have. If you
are not careful you will damage the board.