iTunes Extras are only available in iTunes purchased movies. What bothers people most is that iTunes Extras can not be streamed with Apple TV, in other words, you can only watch iTunes Extras with iTunes on Mac or PC. You can follow the below instruction to find M4V files in iTunes Extras and then add them to iTunes to be synced with Apple TV for playing.
How to find M4V file in iTunes Extras
Right click iTunes Extras file in iTunes and choose Show in Finder from the contextual menu. Then two files — its main movie file (.m4v) and an iTunes Extras file (.ite) will be showing.Right-clicking the .ite file and you will find Show Package Contents option in the contextual menu. After choosing that, the iTunes Extras file displays as a folder, where the various and sundry media, CSS, and data files that make up the iTunes Extras experience are bundled together. Open the Videos sub-folder and you will see the enclosed .m4v video files.
How to watch iTunes Extras on Apple TV
Drag the M4V files you found by using the above method to your desktop. Then, drag those .m4v files into iTunes and now they are ready to be streamed to your Apple TV.
Another way to watch iTunes Extras on Apple TV
It is very troublesome to find M4V files in iTunes Extras and then stream them to Apple TV. Here is a simpler way to do that. M4VGear can automatically check iTunes Extras without finding M4V files and convert them to videos that can be watchable on Apple TV. You can refer to the following link to learn more details: http://m4vgear.com/guide/how-to-watch-itunes-extras-on-apple-tv.html.