My cat just fell out the window...

So basically you are teaching your cat that when she wants to go outside she just needs to poo on the carpet....

Never, ever shouts at your cat. I mean it.

i know it is unbelievably frustrating, but unless you actually catch you cat in the act, they will not associate being shouted at with pooing on the carpet. moving the litter tray closer to the door then outside is by far the best bet.