You're looking to remove them and fill the holes presumably?
If you put the screw back in so that's it proud of the plasterboard by say 5-10mm then you can give the screw head a few taps with a hammer, thus reversing the compression of the fixing which should allow it to be removed.
Or use a countersink bit to remove the head.
Or use some long nosed pliers to prise off the head.
If you have the original machine screws you can screw them in slightly and then hit the screw with a hammer to straighten up the wings. You can then use pliers to grab the screwhead and pull the fitting out.
On occasion, I too use a drill bit slightly larger than the screw hole. As you drill through, the visible collar will fall off.
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