Some things happen as a result of regular background jobs. You might need to wait a day for changes in trust level to be reflected in the accounts.
With the default setup, people will enter and leave TL3. So it’s normal for a person to join the group and get the badge, and then later to leave the group and lose the badge - I think.
That is, the highest level achieved would be TL3, but if you lost TL3 because you became disengaged, you would normally lose all the signifiers that you ever had TL3. I think.