GMail plug in shows old tasks that were completed before (27 days, 23, 18 days old). These tasks don't appear in Android, Mac or Chrome webapp.
Please try to go to Chrome's Advanced Settings -> Content Settings -> All cookies and site data, search for "Todoist" and delete all Todoist-based entries, reload the browser, log back in and let us know if the issue persists.
I have done that recently for another issue. I am seeing this issue on GMail after clearing the cache.
Please tell me - does deleting these tasks make them disappear or do they still pop up next time you reload the browser?
Deleting them makes them disappear. The don't re-appear when I reload the browser.