If you could provide some packet captures from the TV, analysis is pretty straightforward...
If I decide to go "deep techie" on this, I'd probably pursue an alternative DNS approach. "Pi-hole" looks very interesting in this regard. I wish I hadn't just gotten rid of my old laptop. (smile)
Something I forgot to mention in my original comment -- that darn TV is accessing the Internet even when it is (supposedly) turned off. It's hard not be cynical about this stuff.