Couple of questions:
1) Is the Inverter on or off when running the Gen?
2) Is the Inverter a pure sine wave?
3) Is the Gen a pure sine wave?
4) Have you tried swapping bedroom and living room TVs? Is problem location or TV?
5) If it follows the TV, are they different models?
6) If yes, see back to questions 2 & 3, some models are more picky about how clean their AC is vs others.
7) If it's location, well, no clue...
There's no use crying over spilled milk, unless it's on your keyboard.