Ethernet over HDMI Ethernet over display port Ethernet via thunderbolt They could probably do something tricky with a driver and serial over HDMI

I don’t know about this one but several LG monitors actually have Wi-Fi built in.

Of course, If it was using Wi-Fi you could just not connect the Wi-Fi. But some manufacturers are getting smart and are able to use open networks to call home. You could open it up find the antenna and short it out directly to the ground plane