How do I remove stuck GU24 adapter from A socket?
The adapter you are showing is to make an E26, edison base, receptacle into a GU24 base permanently. Note the tab on the thread side. So it's not made to be removed. These are usually installed to satisfy an energy code requirement. 

Oddly enough they make an adapter to convert a GU24 back to a E26 if you would like to try that or you could replace the socket with a new one if possible by rewiring the fixture. Or you could just try working it out of the socket like the first one you did.

I know this is not much of an answer but maybe it could point you to the right direction. Good luck