There is no UI to do this. You'd have to delete session.json file before every startup. that will also kill an open tabs.

Thanks! Was able to delete it and things are back to normal

Same problem: Thunderbird opens with Quick-Filter already applied with a previous search. Version is 68.3.0 (64-bit) on Debian 9.

Tried clearing value and closing/restarting app, with no success. Eventually searched file system for the search-term that was being pre-populated into Quick-Filter and found it in session.json. Closed Thunderbird and removed the word from session.json. Seems to have fixed it, but now Thunderbird is not remembering Window position from last session. Renamed session.json as session.json.bak and restarted Thunderbird. It did recreate the file, but still seems it can't remember it's previous Window position. ... well, still better that starting with a filter in place.