how to remove purchased apps from apple tv 4 ?

Post author didn't mean how to delete the app from home screen, but how to clean it out from Purchased list from App Store.

I have the same problem because when I hadn't set the password for App Store to be always on, my kids were able to download all kind of games, and now when I clean them out, they are able to download them again from the Purchesed list, because it does not require the password anymore.

No, the OP was referring to removing from the home screen. You can't remove purchases, but you can hide them

Hide and unhide iTunes Store, App Store, or iBooks Store purchases - Apple Support

It's very similar to all iOS devices:

navigate to the app you wish to remove

click and hold the big top button on the remote until the icons wiggle

whilst icons are wiggling, select the one you wish to delete, and option appears "do you want to delete "

This didn't work for me. Only the one I selected wiggled. I had to hit the little screen button before a delete option showed up.

Just for reference, this is described in the manual here https://help.apple.com/appletv/#/atvbad14dc6a .