If you want to move a touchpoint to a different team in your organization, you can do it in the touchpoint view.
Go to Collect then Touchpoints
Select the touchpoint you want to move
Click on the touchpoint
Below the Select organization team, select the desired team you want to move the touchpoint
Remember to save your changes
Note:
In the touchpoint view, you can check the team each touchpoint belongs to. So make sure you made the changes correctly!
If the Select organization team dropdown menu is missing then your account does not have the rights to edit team structures, in that case contact the admin that invited you to the organization