That's not a set phrase, but just a variation of a structure A を B と思う "to think(or consider, judge, interpret, etc.) A as B".
e.g.
彼女は彼(のこと)を英雄(だ)と思っている。
She considers him as a hero./She considers that he is a hero.
何の~も is for complete negation in a negative sentence, and ~のこと is used there to make clear the direction of emotion, as in 彼女のことが好きだ, 嫌いだ, 憎い, うらやましい, etc..
を at the end of a sentence shows that it's an inversion, or the following part is omitted since it's obvious from the context. It seems to me it's the former. The preceding sentence is 知らないのだ or like that, isn't it?