She should invite students to discuss any problem openly, one on one or in small groups, promise to act on them but firmly condemn the culture of anonymous mails.

She should update the students about the efforts the institute is taking in sprucing up the syllabi, hiring talented faculty etc., but make no reference to the letter.

She should convene a meeting of the faculty at the earliest and get them to work on updating the syllabi and also arrange a faculty development program but keep mum about the letter.

She should convene a meeting of the faculty and talk about the letter as a symptom of a deeper malaise, ask them to update the syllabi and also organize a faculty development program.

She should ignore the letter and not think about it at all.