How to delete purchased movies?

Welcome to the Apple community.

The purchased list on your Apple TV is a purchase history, you cannot delete history. All you can do is hide your purchases from your purchased list, which you can do at Quicklinks > purchased, in iTunes on your computer.

I've had items deleted from my purchase history by calling Apple tech support and telling them which items (certain movie titles, in my case) to delete.

As long as you know that they are now gone from your account, from all devices.