RTH has nothing to do with the transmitter (controller) GPS. That is only used when doing follow me, etc. RTH uses the home location set when you started up the drone. If you did not see that message, then you do not have a RTH location.
You could tear the GPS out of the controller and it would have no affect on how anything about the drone worked.
That's not true. If the RTH is set for Dynamic then the controller has a lot to do with the RTH.