Hi Chris,
This is a great question, that points out the documentation needs improvement in this area. So thanks for posting it here.
On your dashboard, go to League Manager -> Teams and click on a team to edit it. At the top of the screen, directly below the team title, you will see a permalink field. You want the last part of the permalink. In your example above, it is probably “wrecking-crew”. I have made a note to add this ‘slug’ as a column on the Teams screen in the next build, so you don’t have to do down another level to find it.
-Mark