I've tried with pliers but it won't budge. Not sure how far up it goes (or what it's even doing there). We just want to plug this hole and paint over it.
Hello @MagpieLark
Welcome to the Bunnings Workshop community. It's sensational to have you join us and thanks for sharing your question about your broken screw.
I suggest looking at using https://www.bunnings.com.au/trojan-250mm-locking-pliers_p0126917 . Set the locking pliers to maximum grip and snap it onto the body of the screw and turn it anticlockwise. If it still refuses to move, I suggest rocking the screw left to right to snap it off. My only other suggestion is to use a https://www.bunnings.com.au/irwin-3-piece-cold-chisel-set_p0591292 and cut the screw body in half. Once the screw body is no longer exposed you can then use a filler to hide it from sight.
Please remember to wear personal protection such as gloves, goggles and a mask when working on your project.
If you need further assistance, please let us know.
Eric
Concurring with Eric - long nosed or just normal pliers - rock it back and forth. It will snap off.
👍️