I updated the Google authenticator app before seeing the warning on Bitfunder...
For the moment I'm still logged on the website, but unfortunately I can't disable 2-FA authentication without providing a valid code (which I can't, since the app update erased my existing data).
What should I do?
Try this...
How to recover:
I recovered from this mistake. This should work on both jailbroken and unmodified iPhones, and will not loose your jailbreak if done correctly (point 5):
1) Swear at Google (OK, most of you have probably already done that)
2) Delete the Google Authenticator app from your Phone.
3) If iTunes sync automatically with your phone, you probably want to turn that off first. Also, if you sync over WiFi it may already be too late - I really do not know.
4) Connect your phone to iTunes. Enable the panel on the left. It shows "LIBRARY", "STORE", "SHARED" etc and also the name of the phone. On newer iTunes it is disabled by default, choose View / Show Sidebar.
5) Right-click on your iPhone, choose "Restore from Backup". DO NOT use the normal restore button on the main window, as that will also restore the firmware and wipe and restore everythin (it will take ages resyncing, and any jailbreak will be gone).
6) After restoring, iTunes will resync your phone and reinstall Google Authenticator. If you did not sync or backup since upgrading the app, the old version INCLUDING KEYS will be back.
7) If jailbroken, install Update Hider and hide the update to GA (I have not done this yet myself, but it should work).