Hi Chef!

You can view Team League info under the My Teams tab on the Chef Teams screen. Any change to Team Leagues as a promotion or demotion will be updated post Team Tournaments. You can also view your team's Trophy collection by tapping on the Trophies icon on the My Teams screen. 

Please note that the Chef Teams Win Points can be seen under the Top Chef Teams tab.

Related FAQ: 
How does a Team get Promoted or Demoted to a different Team League?
What are Team Leagues? What are its benefits in the game?