Screen fasteners with round hook

This is one old screen clip. Just looking at the style I don't think this has been made in a long, long time. We have a couple that are similar based on just the design, like our 70-001 and 70-029, but these are usually meant to work as latches, not so much retainers, like yours.

You may have better luck with something like our 70-132 or 70-164, or maybe even a plastic clip like the 70-180. These three parts install using a 70-112 thumb screw, or you could probably just use your old screws if you still have them. 

Sorry that we couldn't find you a better option!