If you are the admin at your service, you have the option to prevent conversations being started between the parents and non-admin teachers at your service.
Click on your 'Menu' button.
Click your service's name.
Click 'Edit' to access your service's settings.
Uncheck the 'Allow teacher-parent conversations' option:
Click the 'Save' button.
Turning off teacher parent conversations will mean teachers can't start conversations with parents at your service and vice versa. Parents will still be able to have conversations with the admins and their family members.