The sentence basically follows the rules of reported speech (indirect speech).
He was wondering (something) means he was asking himself (something) — similar to He asked.
Direct question (quote):
“What prompted him to take no notice at all?”
When you report the question above, prompted has to move back a tense to the past perfect: He was wondering what had prompted him to take no notice at all.
He was wondering what promted him to take no notice at all - is it always incorrect?
Could it be so that the direct question was: “What does prompt him to take no notice at” in the sence that he usually takes no notice at all. And in this case you can use Past Simple instead of Past Perfect, can’t you?