How to seal air vents where I suspect roaches are coming through?

I have wire mesh that I was going to attach to the inside of the vents, but the vents will still have a gap around the edges (old house) (pic in comments).

Since the gaps between the vents and the floor are big enough for a roach to crawl through, I assume the mesh won’t really stop them, although I guess it might still help.

It’s a rental so I can’t make any seriously permanent changes.

(I’m talking about big ass American cockroaches. Palmetto bugs, water bugs, whatever you call them, that typically live outside but often wander inside. I can deal with any creepy crawly slithery scuttery thing, EXCEPT PALMETTO BUGS. Instant primal terror mode.)