Odds are that she eats more when watching TV because she's distracted and not thinking about what she's doing. On one hand, good, because it gets her to eat. On the other hand, not so good, because she isn't paying attention to her body. She might not notice when she's full and may keep eating because she's distracted. It may be a good short term solution, but you may be setting yourself up for issues further down the road.
I know it's hard, but try to remember that toddlers really don't need very much food to survive. They can eat in spurts too...nothing for several days, then act like a bottomless pit. And it's totally normal. Weight gain slows WAY down so they just don't need as much food (of course, losing weight isn't normal). Healthy kids don't starve themselves. I promise!
I haven't seen your other posts, but if you have visions of sitting down at the table as a family with no TV, your best bet is to start that habit now. Believe me, trying to break a food/TV association will be a LOT harder later on down the line. She may not eat as much, but it's probably because she's paying attention to her body and not eating past full. Does that make sense? I know how hard it is to watch your child survive on air, but if she's healthy, that means she's getting what she needs!