You appear to have a mounting system known as a tap-in hinge. The hole that is drilled is a little undersized for the ribs on the metal inserts, so that when the two posts are pounded in, they stick in the holes tightly like a ring shank nail. When you want to remove the hinged part, you are supposed to be able to simply unscrew the two screws, and the posts are supposed to stay in the hole for remounting purposes. I don't think the green plastic part is the problem. If the screws didn't back out when turning them counter-clockwise, they might have been over driven when first installed and are jammed onto the metal inserts, or the inserts are turning in the hole. If that is the case, then there is not an easy way to demount the hinge. You might be only able to get it off the way you did, by brute force; but, unfortunately, that sometimes damages the hole and it may not be possible to get new posts to securely mount in the hole because of that. As an experiment, I suggest you try unscrewing the screws for other hinge mounts...including ones you don't want to replace as a test to see if any of the other ones uninstall normally. Here is a video that shows how this works for a similar hinge mounting system:

https://www.youtube.com/watch?v=7ekKXVvN6Gg

One other thing: with the hinge plate you are holding in your hand, you should be able to put a pliers or ViseGrip on the insert part and then unscrew each screw, preferably with a cordless driver. Whether you can remount the plate securely by reusing the inserts or getting new ones is the question.