To change the Sports Season navigate to:
  1. School Website > Website Management > Websites > Name of Site 
  2. Find the Page the Team Picker is on
  3. Click the Wrench Icon
  4. Click Edit Page Content
  5. On the Team Picker Content Type, click the Gear Icon and change to the Season you want to display (you can select all seasons as well)​
Don't forget to also change the Header, etc to reflect the correct info if displayed the old season name.