Here is what I did.
A. My environment
A.1. When I open Firefox I will sign to my google account automatically
A.2. I have 2-factor authentication with google.
B. What I did
B.1. Logged out from google account
B.2. Changed login name and password in gmarks options to some random values, e.g. "z" and "m".
B.3. Restarted firefox, now I see sign-in option in gmarks menu
B.4. Logged into my google account and regenerated gmarks access password
B.5. Signed into gmarks account with generated password and it seems working again.