(Thank all of you for the responses to my older cat problems.)

The other three are younger and regularly go outside.  I'm the obliging
doorman for them more often than not.

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.

The annoying part is that they're smart enough to learn this, but not
"smart" enough to come to the front door if they do this when the weather is
bad.  They want me to open the corresponding window for them.  Two of them
got left outside the other night

I need a cat door.  More precisely I need a window door that can be held in
place with the upper sash.

I've tried yelling at them, which pretty much just makes them run in the
door fast.  I tried not responding immediately which gives them ample time
to figure out new screen-mangling techniques.  I tried a spray stay-off
agent that doesn't have enough surface area on the screen to be effective.
This past summer I sprayed them with a water bottle, but they don't make the
kitty-synapse connections that the screen thumping is the bad behavior and
not the alerting me to come in.

It's also frustrating when the male rattles incoherently to come inside,
squeaking his paws on the storm door glass...and runs directly to the
litterbox.  I'm thinking his bladder would burst before he'd spray outside.