In order to delete a PermissionGroupFolder you would need to ensure that there is no PermissionGroup entities associated in the children.
Example
DELETE
<ServiceRoot>/Sites(‘MySiteAlias’)/Plants(‘PlantA’)/PermissionGroupFolderChildren(‘idToDelete’)
<ServiceRoot>/Sites(‘MySiteAlias’)/Catalogs(‘CatalogA’)/PermissionGroupFolderChildren(‘parentFolderId’)/ChildFolders(‘idToDelete’)