The lower-case abbreviations "tv" and "th" are used for addresses in Danish apartment buildings, for "til venstre" (to the left) and "til højre" (to the right), respectively. As in 2.tv meaning on the second floor above the ground floor, to the left. (Ground floor is abbreviated "st." for "stue".)
"to see TV" doesn't make any sense in English, though.. Does it? Of course "se" can mean both "to see" and "to watch", but "to see" is incorrect in English in the context of watching TV.
Nothing wrong with see. Duolingo makes many many mistakes in Danish, you need a new voice in order to vary the lessons and to pronounce a great number of dialogues correctly. I know, I am Anglo Danish and I am disappointed that the lessons have a far lower standard than the other languages I follow