Earlier quoted context omitted.
It stops listening. No action required. You can check in the Alexa app what is recorded (I just did). You can also check what is sent out to Amazon (which is what I did when I got the first one, using wireshark). The hardware is listening all the time, for the wake word. Nothing is sent until a wakeword is received.
That's exactly what Amazon would like there users to think. How do you think he wake work is detected? It MUST be listening to some sort of ambient audio, wether that is recorded or kept in anyway, only Amazon would know.
PS I'd love to call mine 'Computer' or 'Hal'.