How to change/reset Google Account password after changing at Google side
I have just changed my gmail password from Google's website. Now Mail and Calendar apps on all my Macs (all on El Capitan) stop connecting to Google. Looking at Console messages, it appears that Google returns 401, which typically means the password used for connection is incorrect. However, I couldn't find out how to change gmail password on Mac. The Internet Accounts panel in System Preferences does not have a change password option. It seems the only option is to remove the account and add it again, but it means all messages would be deleted and downloaded again on all my Macs. I wonder if there is a better way? Isn't this an obvious oversight on Apple's side to miss such an essential feature?
MacBook Pro (15-inch Early 2011), OS X Mountain Lion (10.8.2)