Often, you can't unscrew them. In this case your best bet is to drill the core out, then remove with a trim removal tool as shown above. The plastic there is pretty soft, so I don't even use a drill: I just turn a drill bit a few times by hand. You want to drill out the head of the core, then the main body will come out with a minimal applied effort (you may not even need a trim removal tool if you don't have it).