What do you mean it “appears” on your TV. Do you have screenshots? Is this a screen cast option you’re seeing? Need more info.

I could see a shop charging 100+. I would suggest doing.a bunch of research on your specific laptop model and doing it yourself. It’s really not that difficult. I’m not liable if you mess up though. But it may be a good learning experience especially if you’re tight on cash.

Why do you think you need your thermal paste replaced on your laptop? How long have you had it, what is it used for, is it filled with dust? A shop may charge 100+ to do this it all depends on what’s actually wrong with it.