You can also deny on habitability limitations (# of people vs # of bedrooms), a consistent no pet policy if they have a pet,  Megan's Law registrants, ex convicts on parole or Sec 8 applications if you do not want to do the work they request after their inspection.

Everything I've read about changing the terms of a lease has to do with raising the rent, or no longer allowing pets, etc. and hasn't really helped giving me a real sense of what to do on this situation. 

My biggest or most unusual problems were: abandoned vehicles, a person escaped from a mental institution, tenants with pet rattlesnakes that escaped their container, a round trip visit to the dentist for a wisdom tooth removal, a one way bus ticket from Kansas to Georgia, cashing $25,000 worth of checks each week for a group of guys from out of state, etc.  

Screens happen to be one of my pet peeves, so I add them to my own annual maintenance inspection checklist.

The seeds are the spiked little things that get stuck in your shoes, tires, feet, pets feet, everywhere!

Other than not having any previous landlords, they meet all of our standards (income, nonsmokers, no pets, etc.).

Contract has provision for pet at home, which comes with security deposit

The Property Manager stated she is a good tenant. xxxx does not have any pets and is willing to do the 2 year lease, as you requested.

This I've seen in 4 generations of NE families.Or you could die and leave the assets to a manager for your cat, lizard or pet pig. 

I'm not risking bringing someone else's parasites, pet dander (or worse), odors, or bodily fluids into my nice vacation rental.