I also use a babysitter, though even more rarely than you. Maybe 5-10 times per year. My rules are basically: spend time with them, try to make sure they eat something, try to get them to bed around their bedtime (a half hour one way or the other is no harm, but three hours later means exhausted grumpy kids the next day.) If they drink soda instead of milk for dinner, or they don't get their teeth brushed, or they watch more TV than they should... I don't worry; it is only one evening in their life. However, if I had a babysitter on a much more regular basis, then I would probably have some firmer rules.
Depends - if you have few rules, and no TV is one of them, then I think the babysitter should have gotten the message. If no TV is just one of a ton of other rules, then I think you should prioritize your rules and let some things go.
I'm not too worried about tv, both my DCs watch. However, you have politely told her twice not to watch TV, so I would think the babysitter could listen to that.
On the other hand, I agree with the others, her house, (sort of) her rules, your house, your rules.
If you like her, and the kids like her, I'd give her one more try, but with a clear message that the TV is NOT OK with you. Then the ball is in your court. If it is a huge issue, and this babysitter is not flexible, then time for you to find a new babysitter. If it is a minor issue, then let it slide.