Jason Travis wrote:
(...)

Problem is I've accidentally reinforced a distressing
behavior. When they were little they would climb on
the outside screens for fun. This of course
brought me out the door. So what they've learned from
this is if they're outside and want to come in, they
pluck the screens to alert me. One screen has been
nearly destroyed, the others they don't seem to abuse
as much.

I think you can get metal screen mesh?

S.