Grab the black plastic cover over the sockets with a pair of serrated slip jaw pliers. Rock the plastic cover side to side by about 10-15 degrees total travel to loosen it. Position the pliers so they only grip about the top 2-3mm of the connector (no pins up there). Pull straight up and off the female pins underneath.
Heat each pin individually and remove with pliers or tweezers. Clean out holes by your desired method. Wick, smack the board, whatever - anything but a spring loaded solder sucker, those things will destroy a board in seconds.