expression
without paying any attention; without giving a thought; heedless of
Used adverbially to describe doing something while completely ignoring or not caring about something else. Often appears in written narrative or formal speech.
See also: 気に留める
彼は周囲の批判を気にも留めず、自分の道を進んだ。
He went his own way, paying no heed to the criticism around him.
彼女は雨が降っているのも気にも留めず、外に飛び出した。
She dashed outside without even noticing that it was raining.
The affirmative form meaning 'to pay attention to' or 'to keep in mind'. 気にも留めず is its negative adverbial form.
From 気 (mind, attention) + に (particle) + も (even) + 留めず (negative continuative of 留める 'to stop, to fix'). Literally 'without even fixing one's mind on'.