By the how the president ...

"Many Democrats regard Mr Bolton as a perfect witness, a respected conservative national security hawk who was nonetheless incensed by the how the president and his inner circle were treating Ukraine, and who broke sharply with the president upon his departure from the White House."

(NYT.)

Is the complement of the preposition "by" the how the president and his inner circle were treating Ukraine a noun phrase or is determinative "the" modifier in the finite clause?