I think I figured it out, probably another low impact bug so low priority for a fix.
It seems to me that when tracking an objective on the trading post the game tracks it across all alts on the realm, while un-tracking it only applies to the one alt you did so on. (Also, clearing an objective does not appear to remove the tracking to it, just make it not appear after checking that it’s complete, so it will automatically show up as tracked again if it is still an available objective when the month rolls over.) So, when you un-track something then log into another alt it will still be tracked and if you then log out with that one still tracking it, when you log back in to the one you previously cleared it from it will be tracked again.
The way I got rid of them without doing a reset or disabling any add-ons was to go through and un-track the objectives on every alt one after another.
Alternately, I then figured out that the Traveler’s Log tracking is saved in your files in the realm’s folder’s “config-cache.wtf” file under “SET perksActivitiesPendingCompletion” and in each character’s folder’s “config-cache.wtf” under “SET trackedPerksActivities.” So going through while the game is off and deleting that line from each file will reset the tracking without having to log in and out a bunch of times.