League administrators can move players easily from one team to another team.  No less you can even make the person being moved a captain, co-captain or player ("role on team") of the new team too.
Here are the steps for moving a person from one team to another:
Log into TennisPoint as the league administrator
Navigate to the Active League Season being managed on TennisPoint
Click on the playing level where the "to be moved person" exists
Click on the "Teams Tab" to view all the teams in a given playing level.
Click on the team name which has the "player to be moved" so that you can see a list of all the players.
On the far right side of each person their is a "drop down menu" of options.... "move to different team"
After selecting "move to different team" -- you will see a set of options for moving the person to a new team.  Yes, you can even move the person to a team on a different "playing level" too.