I'm speaking of the second Time-Turner she has had, in the Cursed Child.
She, of all people, knew the dangers a Time-Turner could raise.
"No!" said Hermione in a terrified whisper. "Don't you understand? We're breaking one of the most important wizarding laws! Nobody's supposed to change time, nobody!
Professor McGonagall told me what awful things have happened when wizards have meddled with time.... Loads of them ended up killing their past or future selves by mistake!
(Prisoner of Azkaban, Chapter 21, Hermione's secret)
I understand why she didn't destroy it, but why hide it in such an obvious place, her office, and protect it only with a "simple" riddle?