Generally speaking, you do not have to take any action after changing your Google password. If you are using Google Voice on your OBi, and it stops working, then log into OBiTALK, click on your device, click on the SP that has Google Voice set up, click past the emergency call warning, and then click the link that says "Click here to replace the active Google account". You will need to be logged into the correct Google account on another tab in your browser when you do this.
Following these steps will regenerate the OAUTH 2.0 security token that gives your OBi permission to access the Chat service on your Google account.
