E Terminal on a Thermostat: Emergency Heat Wiring
E turns on backup heat without the heat pump, for when the outdoor unit fails. On many systems, E and AUX run the same heat strips and are tied together at the air handler.
ecobee and the Amazon Smart Thermostat have no E terminal: emergency heat mode uses the aux heat wire instead. If your E and AUX wires land on the same terminal at the air handler, the E wire can be capped. If they go to different places, get a pro to confirm before capping it.