She delicately alluded to his bad behavior.

Literal

She [topic-は] his [genitive-の] misconduct [at-に] indirectly touched.

ふれる (触れる) literally means 'to touch,' but extends figuratively to 'to touch on, mention, allude to (a topic).' The に marks what's touched on. それとなく ('indirectly, vaguely, subtly') is an adverbial expression for hinting at something without naming it — perfect for delicate matters. The combination of indirect ('それとなく') + light touch ('ふれる') paints exactly the kind of polite, oblique reference Japanese culture often favors when bringing up sensitive subjects.