To get it out, either grab the head with a pair of needle nose pliers and carefully turn it out while gently pulling, or use a pair of diagonal cutting pliers to put a little pressure under the head of the screw while turning with a screwdriver.
After you get it out you will need to drill the hole and glue a wood dowel into the hole. Drill bit size coresponding to dowel size of course. There are some very small dowels sizes available at the hardware store. Carefully make the dowel flush with the head, then redrill hole the correct size for the screw.
I have done this to an entire set of tuners that I changed out and you cannot even tell that the holes were doweled.