Hi Mariachi, the recommended controller T1D would not use a WiFi signal but Bluetooth signal. Thus it would not boost the wifi signal between the mobile phone and Tello.
Remote controller T1D is connected to Tello via Bluetooth and it doesn't give extra range. But with T1D the recorded video quality and FPV video link is worse. Proof link: (+ read the commnt).
Controller dont help in extending range. Recommended T1d controller uses bluetooth to connect to mobile.. mobile to Tello connection is still via WiFi. Other know method to increase the range is to use a Wifi repeater like Xiaomi v2.