Sorry, but it won't work. And here's why:
The flame arrester screen rotates around behind those little tabs due to harmonic vibrations of the engine. The screen, being metal, and the housing, being plastic...this "action" wears the little tabs down to the point that...yes, you can pop the screen back in but it will soon be lying at the bottom of the housing again.
What I did when I had a fleet of about 50 of these was to use a #4 sheet metal screw and thread it into the bottom of the housing where a little pointy sort of "tongue" or lip is molded in. If you put the screen in and then start threading the screw into the housing at an angle so that it snugs up against the screen when it bottoms, it won't come out again. As a precaution I also got into the habit of putting a dab of 3M industrial adhesive on the protruding threads but I have never seen one back out, glue or no glue.
You can glue the screen back in but the oil and gas fumes the engine "burps" will eventually cause that interface of plastic to glue to metal to break down.
Or, you can buy a new muffler. But, you've already seen what happens over time to that expensive little piece.
Good luck.