More info as follows.
This problem - the "Reconnect to Google" email which doesn't lead to an effective re-connection has been persistent for me for the past several days. It applies to two separate accounts on the same Win 8.1 machine, and to the only account on an old Win XP machine. The recommended solutions above in this thread DO NOT WORK, as any engineer worth his or her salt could have verified any time. Strangely, one of the solutions - to disconnect the Google account completely and to reconnect, did remove another anomaly, as follows. On my Win 8.1 machine, my Live Mail Contacts account, which syncs promptly and reliably with Win 8.1 People, acquired a while back an almost complete duplicate set of names and phone numbers. These showed up also on a separate list on Live Mail contacts under the "Social Network" heading. I could neither delete nor edit these duplicates, Live mail contacts Clean up didn't touch them, and they didn't go into Win 8.1 People, so they were sort of "Ghost" entries, but a nuisance. Disconnecting the Google account completely and reconnecting it cleared them straight away(!?!) Maybe there's a clue there. Also, maybe connected, I am not on Skype, and I don't want to be. Windows People acts as if I am. It tells me I have a Skype ID, and it tells me who of my contacts are on Skype. To call this intrusive is an understatement - in my view it violates my privacy and theirs. I can find no way of making this go away, but the ghost Live mail category of "Social Network" has kicked off my paranoid suspicions. Apart from that, it's my view that Microsoft, with all its resources, could easily diagnose these problems and fix them - if they were motivated. ****, they might have to talk to Google, which wouldn't really hurt, would it? To allow this disfunctionality to linger seems more like corporate gamesmanship than incompetence to the paranoid part of me, aimed as it seems at sabotaging critical interoperability between Windows and Android. What have we got to do to motivate Microsoft to fix this?