The PTE has a dirty bit that indicates if it's been written to, so when the OS evicts the page from RAM, it writes it into disk instead of just discarding it.

But the PDE(which might contain dirty PTE entries) doesn't have any dirty bit as far as I can tell, an Accessed bit at most(which doesn't tell anything about dirty status, just that it's been used in translation).

Then how does the OS know whether to discard or save the PTE table the PDE is pointing to, when paging it out of RAM?