They may give you a hard time about that if you go to rma it.
Good point.
It may be that the best strategy would be to re-install the other plastic mount with both screws, and use a pair of diagonal cutters to VERY CAREFULLY cut-away the plastic mount around the stuck screw. If you have a soldering iron that you aren't emotionally attached to (because plastic absolutely destroys soldering iron tips), you can use that to VERY CAREFULLY melt-away a lot of the plastic to make things easier.
Remove that processor from the socket, first, though.
Once you get the actual head of the screw accessible, you can use Vice-Grip pliers to get a good hold on the head of the stuck screw, and remove the screw from the back plate. Once you have the screw free, you can un-screw the other screws that you previously re-installed (which were re-installed just to stabilize the bracket and avoid damage to the motherboard), and remove the back plate.
At that point, you should inspect the threads of the post where the screw was stuck, to see if there is thread damage. If the threads are damaged, you can use a correctly-sized tap to re-establish clean threads, by running the tap through the threads from the bottom of the threaded post--use cutting oil on the tap, of course.
Once that's done, clean up the back plate with isopropanol, and return to the task of installing your cooler of choice.
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