You don't.

If you don't use Thunderbird's password manager then it won't store passwords. But if you went to Options|Security to remove a password then you are using, or have at some time in the past used the password manager.

If I take what you've written at face value then you appear to be contradicting yourself.

In principle, if you go to a mail provider's website and change a password there, then when Thunderbird tries to connect using a stored password it will fall and should ask you to provide the new one.

Are you not being prompted for a new password?

OK, I understand what you are saying. I may be mixing up the Password Manager, with the Master Password application, where you have all the passwords stored under one master password. The latter I do not want to use. Thanks for a more explanatory reply than the other one. DCM

I don't know why it's so difficult to get a correct answer to this question. I had the same issue and I finally solved it myself:

Go to the main TBird menu in the upper-left corner.

Click on "tools" --> Options --> Security --> Passwords --> Saved Passwords.

Make sure you select the "show passwords" button in the lower-right corner of the pop-up. All of your saved passwords should be visible. You can then right-click on any of the passwords to edit them.

The OP did not want to use password manager so I fail to see how your answer is relative. If he asked how to see the passwords saved in password manager then you have the correct solution. I don't know why it is so difficult to understand a simple question.