You will asked how much you have been damaged and why you returned the deposit without a proper inspection, why you did not inspect for pets earlier, and to prove she had a pet when she might just deny it. 

If I wasn't good to her, she may have ignored it and tried to deny that she did it when she moved out.

If you think you will have better options if you wait then I would deny them.

However, it seems that the majority of people here are saying that it is worth taking the loss in order to find a better tenant.I will run the actual tenants history through Smart Move and if it comes back very weak then I will have to deny them, even though they have a strong cosigner.

Show up on the date and if denied entry give a perform or quit and another NOE (prepare the notices in advance so you will have them handy). 

Once the cats out of the bag that you are the owner, it will be much more difficult to deny unreasonable requests. 

Which, of course, gave me a legal reason to deny them - for not completing the application or for giving me false info.So, I'd charge them something, even if it was $10.You could always say it will be refunded if they're approved.  

If Landlord verbally notifies Tenant a minimum of 8 hours in advance of a showing of the Premises, and then, Tenant denies access to the Premises or the Premises are not in showable condition, then Tenant will be charged $125.00.

Deny.

I think their application will be denied...