What should a man do if he has doubts that his wife is not lowering her gaze?

The fundamental principle is that a Muslim is innocent and free from فسق (moral corruption). It is not permissible to spy on a Muslim, based on Allah's saying: "And do not spy," and the Prophet's (peace be upon him) saying: "Do not backbite Muslims, and do not seek out their faults." However, this does not mean that a husband should leave his wife unchecked. Rather, if he observes anything suspicious from her, he should advise her, explain the ruling to her, remove the causes of corruption from his family, and provide them with a righteous environment.