T-Mobile updated the progress tracker for software updates on its website to reflect that the Android 5.0 Lollipop update for the Galaxy Note 3 was being tested by the carrier. It was the second step of a three step process which ultimately delivered this update to Galaxy Note 3 owners on T-Mobile. A changelog posted on Samsung's website confirms that the carrier has indeed released Android 5.0 Lollipop for its subscribers that own the Samsung Galaxy Note 3.
Apart from bringing all of the improvements that are part and parcel of Android 5.0 Lollipop, this update also brings improvements for the Wi-Fi calling experience on T-Mobile, resolves IPv6 email setup and also resolves issues with one way audio on a Wi-Fi call. T-Mobile is now rolling out the Android 5.0 Lollipop update over-the-air for all of its Galaxy Note 3 owners.