Anyone who is a Pobble administrator can manage who is part of your school on Pobble.
If you're an administrator, click your account icon in the header, click 'School dashboard' and select the 'Team' tab. In your team list, click the action button (the three dots '...') next to a colleague's name and select 'Remove from school'.
The teacher will no longer have access to your school. Their general account remains active, so they can still use it to leave comments or join another school.