Surround the monitors with strips of infrared LEDs. To the naked eye it will just look like trim, to the cameras the LEDs will be glaringly bright and, depending on the strength of the IR LEDs, obscure the recording of what's on the LCDs. It will take some experimentation to get the effect you need.
To see a small example; look at the end of a TV remote, push the buttons, you see nothing. Point the remote at a camera/phone, push the buttons, you see the IR LED. Most small cameras do not filter out IR.