What you just did is the best way to re-assign teams here. Unfortunately, we all didn't realize this in the earlier days of the site when we would simply type the name of the team over the old team. Sometimes that would reset the TID number, but many times, it did not. The strange part is when one pulls up the card, and clicks "edit team", the TID that displays looks correct, but that's not what is in the backend of the database.
In this case, you saw that TID #302 associated with three teams - this is the exact scenario I alluded to - name changed, but TID never changed.
When I need to updated a team, I always go in, delete the team name, and then select the correct team for the dropdown list. This ensures the correct TID gets assigned to that card. Yes, it is a couple more steps, but it always works.
-- Dan --
Note: Please see my profile for more info regarding trading (section updated 3/4/2024). I have added a large portion of my inventory to the site, and currently have trading turned on (details are in my profile).