u/double_positive

This vent is over my counter top in the kitchen. Any ideas on how to fix and secure the register back to where it won't fall? The inside duct doesn't allow for deep screws on one side and both screw holes are worn/damaged. And not sure why it was set like this in the first place... I noticed it loose a few weeks ago and removed the register completely.

I did try wood glue (still remnants present) but that didn't hold and I was worried the register would fall and damage the counter causing a bigger more $$$ issue.

Penny for scale, square holes that pass through it completely, not sure the type of wood but it's very hard. No flexibility at all despite the holes.