The Apple TV box cannot be reset or operated through a mobile device directly.
There is however a software remote on iPhone, in Control Center. Set up the Apple TV Remote on your iPhone or iPad - Apple Support. There are some requirements, such as both devices being connected to the same home network, and the Apple TV not being too old of a model.
maybe 3rd gen, not sure
Identify your Apple TV model - Apple Support
Find your Apple TV model number - Apple Support
ask to move the icon
“Editing the Home Screen” should be a status for long pressing the select button, not for single short pressing a button. Please account for that difference in how you press buttons.
Customize the Apple TV Home Screen – Apple Support