Chandelier socket removal for arm replacement
That bracket is riveted on. You could drill it out, but you'll have no good way to reattach it to a new socket anyway. Often candelabra sockets come with pre-attached brackets like that (sometimes threaded for a pipe nipple, other times slotted for a screw - hard to say which that is). Best option would be to remove the whole thing together if possible and try to find a matching one at the hardware store (I know my local store has a good variety of such sockets with attached brackets from Servalite). You shouldn't need to drill out the rivet to remove the wiring.