Hardware that can spoof mA usage or cause it
It depends how 'smart' the device is that's detecting the TV power draw.
It may be detecting the current magnitude. In this case you can connect a series combo of an X-class capacitor, and a small resistor to protect things from excess current surge at connection. If most of the voltage drop is across the capacitor, then very little power will be dissipated. Most (all?) consumer electricity meters are smart enough to charge you for only the small power loss in the resistor, not the large VAr provided by the capacitor.
It may be detecting the power drawn. This is unlikely in a cheap go/no-go device, as it means detecting the time average of volts*current like your electricity meter does, but it's still possible. If that's the case, then you've got to draw the power.