I honestly always cringe whenever they thank anyone. I just want candidates to get to the answers and all that thanking takes up valuable time.

With that said, they should thank the screen. You have to think of them on a stage and the debate itself a performance. Performance isn't about reality but creating reality. It is realistically nonsensical to thank a television screen whether or not the persons image is live anyway. It is an illusion, they don't see you through the screen they see you through the feed. So thanking a screen on a talk show when someone is on through satellite is as nonsensical as thanking a pre-taped video on that same screen.

So it would make sense to thank the screen and not the audience as the illusion is that they are talking through the screen and not the audience.

I'm right with electiongeek on this one. Proper etiquette should dictate that the candidate answering the question should thank the person asking the question. After all, they are probably watching. Move quickly into the answer though. Don't linger with exclamations of how great the question was.