Thunderbird does not put anything in the "offer" section. It does not have one. Your account however may have an offers folder and your provider may well be sorting mail into it.

Who is the mail provider? Google have settings here to disable the use of a tag they call "Promotions". https://mail.google.com/mail/u/0/#settings/inbox .

Sorry, but the problem isn't limited to this folder. The fact that the message was placed there isn't a problem and may be fine. The problem only occurs when I try to move these messages to the INBOX folder. The same applies to any other folder I've created. And then these messages disappear!

I am not playing 20 questions. I need to understand how the messages get to the folder they are in and your reply does not help in that. How do they get to offers? if it is a server rule are you fighting it by putting the message into the inbox. 1. What mail provider to you use. 2. Does this madness stop if you turn off whatever they call their implementation of a "priority inbox". That is any de-clutter tools mostly but I find when the user is trying to put things somewhere that the server does not like they have a tendency to disappear. Sometimes permanently.