The Turner Watch is built to cleverly ghost its bluetooth signal when it's connected to your phone. This stops anyone else from seeing it in their bluetooth settings while you perform - it also makes it impossible for anyone else to connect to it.
To change device you will need to forget the watch from the first device.
How do I forget the watch?
First, unpair the watch from your NKTW app. Tap "Unpaid Watch" in the app's dashboard screen.
Then, navigate to your phones settings. Head to "Bluetooth" and find the Turner Watch in the list of known devices. Tap "forget device."
Finally, open the NKTW app on the new phone and paid as normal.
What if I do not have my old device?
Perhaps the original phone is not with you and you need to connect to a new device. To do this, you will need to hard reset the watch. More info on how to do this can be found here: Hard Reset Your Watch.