How can I disable the AirPlay option?

Is there a way to disable AirPlay on iOS devices?

My little girl loves watching her shows on her iPod Touch, but occasionally hits the AirPlay button by accident and then when she might hit the Apple TV option trying to get rid of it - send the screen blank.

I've tried logging out of iTunes store and Home Sharing. Pesky icon stays there.

Is there a way to do this?

Thanks in advance for the help.

Michael