By Past perfect, TOEFL

Thank you, Tam, for the effort you made to try to let me understand this structure. However ... Tam Sadek wrote: Perhaps this example using the Past Perfect/Past Simple will make it clearer. "We arrived late because our plane had been delayed" versus "We arrived late because our plane was...

The TOEFL book is right, Anon. Had had is the past perfect of the verb have (here appearing in its causative use, to have sth done), and is OK in this sentence.