The app is only used to configure SugarPixel and perform remote functions such as setting a remote snooze, doing a software update, or a factory reset. So the app can be installed on any phone that you choose and does not need installed on the same phone as the CGM.
Because SugarPixel uses a secured pairing method, it supports a maximum of 6 apps on different devices to be paired to it. If you exceed 6 paired phones and need to use the app on a new phone, you can perform a factory reset to clear the existing paired devices.