Hi,
That flame trap screen is supposed to be held in place by small "tabs" molded into the plastic of the muffler box.
Over time, the combination of the acid and/or other chemicals in the crankcase vapors plus vibrations causes the metal of the screen frame to erode those little tabs down causing the screen to come completely loose.
I used to secure the screen with a tiny sheet metal screw installed in the plastic at a slight angle to the screen to wedge it in there. And, while I've never known one of those "bush fixes" to fail, I have since decided that it isn't a good idea.
Because, if the screw were to ever work loose, there is a high probability that it could be injested by the engine. If that were to happen, some major engine damage would likely occur. Not worth the risk.
Therefore, the only safe way that I know to repair that failure would be to replace the engine side half of the muffler cover. Item 2 in the link. About $40 plus shipping from boats.net
I have thought about finding a reliable glue to hold it in there but haven't tried that. You would need to "rough up" the surface of the plastic to give some tooth for adhesion but there's usually enough of the tabs left to hold the screen in place while the glue cured.
If the tabs are too far gone to hold the screen, you could still use my little screw trick to hold the screen while the glue dried but remove the screw prior to reassembly.
If the glue were to fail, it wouldn't hurt anything as the screen would simply fall to the bottom of the box just as you found yours.
Just an idea.
Please let us know if you come up with a better way.
Good luck