You wouldn't have volt meter to somehow measure the actual voltage this thing is outputting, would you? Fully charged note 3 battery is at about 4.2 v, if that thing doesn't have sufficiently higher voltage, it won't charge. Once I bought this cheap USB car adapter, it wasn't outputting enough power, so the phone would start charging, the load would drop the input voltage to lower level, the phone would stop charging, the input voltage would go up and it would start charging, until the voltage would drop again and etc. etc.
Try charging when the battery on your Note is low , like 5-10%, it may work then.