Thank you so much! Yes, removing it from the top of my Login Items, in System Settings, fixed the problem.
The article is a bit confusing though -- not only did I never add it via the Dock, but I never could have because Tunnelblick does not ever appear in my dock. And the instruction to remove it is similarly impossible, because it relies on Tunnelblick having a dock icon. So the support article might be out-of-date? (Unless I at some point disabled an option for a dock icon, but I don't see anything in preferences that would suggest that.)
Also, I've been using Tunnelblick for years (on the same system), and this only started happening a couple of months ago, and I certainly never did anything to add it manually to my Login Items recently. So just in case an automatic update might have had a bug that erroneously added it? I am on the beta channel. Just in case you start getting other complaints. (Or maybe just something weird on only my system, in which case never mind.)
Thank you again!