Checking the user group permissions, it seems that "Manage (move, merge, etc.) thread by anyone:" is used to control whom can merge posts, despite it being for threads and not posts. If I remove this, then they cannot do any thread moderation.
Since you are essentially editing post(s) when you merge them, I would have thought that "Edit post by anyone:" would have been the permission to manage this. And my moderators do not have this permission.