HD is not just one type of video file. There is a 720p version and a 1080p version. I ahve a ist generation iPad and I can only put 720p movies on it not 1080p
If you downloaded form itunes then you need to go into preferences, Store
Select from the drop box When Downloading High Definition Videos, prefer 720p
Then go to itunes store. Click on the Purchased link under Quick links on the right
Select TV Shows and find the TV Show you want. It will have a cloud icon by the side of it just click on that and it will download the 720p version at no extra cost
Then when you choose to sync your Iphone will automatically get the 720p version rather than the 1080p version which does not work.
You do not need to delete the 1080p version as itunes manages both side by side and only syncs the version your device can handle.