Do you charge pet fees (refundable or non refundable) and/or pet rent?

Dogs, pets, do damage.

In the lease I didn’t add a pet clause which is my fault.

Also, as an owner of PM Company managing over 1k doors, we have great policies that work for all types of pets.   

She had a no pet clause yet unbeknownst to us brought a cat in.  

Additional complaints include old kitchen tiles not being perfectly white anymore, requests us to bring mop, buckets and scrub it in his presence with extra effort. 3) Upon visiting the property to take note of his complaints, we notice he has brought in an unauthorized pet cat, a violation of lease terms (lease states NO ANIMALS and a violation would result in a $25 penalty per day per animal)Owners want him out and are upset about the cat, specifically because wife is deathly allergic. 

About 70% renters have pets, duplexes come with yards and appeals to more renters.  

Should I still wait for a tenants who doesn't own pets?

You are parroting some kind of a left-wing talking point. 

Remember the Pet-Rock, yeah.