I think that any conditions pertaining to a rental or lease should have been specified beforehand.
Without a lease or rental agreement in writing there is little the property owner can do.
Personally, my response at the next renewal would be something like "I will continue to be unreasonable while you get used to being homeless", or perhaps a 100% increase in rent with a stiff damage deposit.
Anyone planning to become a landlord of a rental property should first consult an attorney versed in contract law. They can help you draw up a lease/rental agreement that is fair, but supports the landlord 100%.You can put almost anything you want as a condition of rental, and more importantly, conditions for immediate eviction.
A pet policy is one of the most important, related to pets/no pets/how many pets/what type of pets (birds dogs, cats, etc.) and specific breeds allowed or disallowed; then you can set a pet fee, either a one-time, or a recurring one, which can be tied into the security and damage deposit.
Not doing this makes it very difficult for a landlord to get rid of a nuisance animal, or to say "you can't have a pet" after the fact.
I have a rental house, which is next door to me so I get to keep close tabs on what goes on. In the 15 years I've rented it, three of the tenants wanted a dog, and wanted me to waive the fee clause in the lease agreement, which I refused to do. It's a $250 initial fee, and $75/year; this is a separate fee from the damage deposit, so I can make distinctions when the tenants move, or I have to make repairs, that the damage was pet-related. This fee is collected with the rent, but the receipt separates the dollar amounts for records purposes. Pet fees are non-refundable, where the security deposit can be fully or partly refunded. These conditions and stipulations have helped me keep the property in relatively good condition, and I have legal basis for any action I may need to take.
My attorney, when she helped us draw up the agreement, told me it was good enough that if I had to evict the tenants, it would make them responsible for any court costs related to the eviction.