Hello compugrrl998,
Thank you for the details of the issue you are experiencing with watching The Walking Dead on your Apple TV. I am sure you are eager to watch it on your television.
Have you tried checking specifically in Movies > Purchased or TV Shows > Purchased on the Apple TV?
Play previous purchases on Apple TV
You need Apple TV (2nd generation or later) to play content on Apple TV. Some features require the latest version of Apple TV software. If they're available in 1080p, you can play previously-purchased 720p HD TV shows and movies in 1080p.
Movies and TV shows
- On the Apple TV main menu, choose Movies > Purchased or TV Shows > Purchased.
- Select the item you want to view.
- Choose Play.
Download past purchases
http://support.apple.com/kb/ht2519
If you are looking there and not seeing the episodes, I recommend verifying that you are signed in with the same Apple ID on the Apple TV that you are signed in with on your iPhone.
Thank you for using Apple Support Communities.
Best,
Sheila M.