For context, I tried going couch gaming for the last few week and kitty decided that the TV was a good scratching post. I'm not as attached to the TV, but still it's painful to watch and I unfortunately can't 'have a talk' with him.
Try to move her attention to something else. Does she have anything to sharpen her claws in?
Every time my cat got close to the TV, and started looking at it closely (as if she's about to do something), I would get her to move.
After a while, she never did it again. And, when I go to work I actually leave all divisions of the house open (except my office, where I have my PC, films, and work stuff), she can move freely, and doesn't do much damage. But, she loves a cheap rug I have in my living room, and that one is a lost cause (whenever she wants to sharpen her nails, she goes on the attack there).
I'm resigned. Since it's a cheap rug, I let her do it, and I'll just replace it in the future, if it ever gets too damaged.
Much of this "misbehaviour" is her way of trying to get your attention.
As your cat gets older, he/she will start spending more and more time sleeping, or resting close to windows, while watching things on the outside.
You need to find stuff to keep her interested.
I have all sorts of cat stuff around because of her:
-she has a place near the entrance of the house, where she goes to eat and drink;
-she has a place to do her "necessities";
-she has a place on the couch, with a couple of small blankets, to rest/sleep (when we are watching TV, she likes to stay there);
-she has a small "bed", in one of the corners of our bedroom;
-she has a "box", where she can also sleep, near the kitchen;
-and she has a cat house in one of the corners of the living room, that she loves to go to when she wants to ignore us (if you ever find one, buy it; it's a cheap one from Lidl, and cats love them, since they love to have a place to remain "hidden"; it's the one below):
