DIAGNOSIS The Google TV interface has a 'Live' tab that's prominent and, by default, tries to tune antenna channels. If you don't use an antenna, it's just a dead button that defaults to a noisy screen.
FIX You can't remove the button entirely, but you can change what happens when you press it. Go to Settings > Channels & Inputs > Live TV. Select 'Set up input' and you can change the source from 'Antenna' to an HDMI port (like your cable box or game console). Now pressing the Live button will switch to that chosen input instead.
IF THAT DIDN'T WORK To change the input the TV starts on when you power up, go to Settings > System > Power > Power on behavior. You can set it to 'Last used input' or a specific HDMI port. This overrides the 'Live' tab default.
HEADS UP The Google TV home screen layout is largely controlled by Google, not TCL. Those top row buttons (Live, Discover, etc.) are baked in and can't be rearranged or deleted like regular apps.