This also means your association dues are higher so it should be a wash.Finally, owning residence in an HOA is a different kind of animal.

Because they cannot find a place to rent with 7 animals?...

I've raised my security deposit requirement to 1.5x monthly rent so I'm covered for 1 month plus some damages if they don't pay last month, and also a cushion for those trying the Emotional Support Animal route to save on a pet deposit. 

I’d just give notice to remove the animals and then evict if needed.  

All I have pictured in my mind is john Belushi and "Animal House" 

Beyond that, the little bit of extra money you're going to get is going to either be a little gravy taken from otherwise great tenants or won't make 5 cents of difference if they get an animal that's untrained or otherwise destructive and they don't do anything about it.

Now you need to start preparing for marketing, showing, screening software and processes, selecting a tenant, Fair Housing, emotional support animals, collecting a deposit, disparate impact, local and state housing laws, Section 8, your lease agreement, late rent, unpaid rent, partial rent, bounced checks, etc.No worries!

Nothing will turn a good tenant into a miserable one faster than a mooching girlfriend/boyfriend or a neglected animal.

He had absolutely trashed the property, and it took quite some time to get the smell out from all the animal feces and urine. 

However we felt sympathetic and agreed to lower her earlier animal damage bill to offset her loss.