You can check to see if its really the Tesla app using power on your iPhone. Go to Settings > Battery and scroll down to see where the Tesla app ranks for power consumption. I leave my Tesla app running all the time and its at 1% power usage, which is 12th in the list (below Siri, FaceTime, Messages and Mail, and only one above Clock!). So, for me at least, the app isnt using any appreciable power (and there is no reasons it should, since all it needs to do is handle the BTLE unlock functions and occasionally call home to Tesla for things like software update checks).