You are starting a new lease with these tenants, so basically you can charge whatever you want, including pet deposits and pet rent (assuming its legal to do that in your state), and increase in rent (again, some states limited how big of a % you can increase it).Its the balance of increasing it closer to market and protecting yourself for eventual damage by having pets in your units vs inducing a vacancy and starting over.....which can be scary but often its a good thing when you take over someone else's tenants. 

@Andrew Syrios and @Kim Tucker Thank you both for great advice in exercising caution when investing out of state.

We asked why and were told that "our client has exercised their right to rescind, Georgia law does not require them to provide a specific reason as we are within the statutory time frame."

@Stephen Bruce In South Carolina, where month-to-month tenancies default to a 30-day notice period with no formal contract, it's especially important to exercise due diligence.

However, that doesn't mean the lender would exercise it.

You can find out how to workout online too, but it’s absolutely nothing compared to having a well-qualified trainer with an exercise science degree (I know because I have one after failing on my own).

Or can you induce seller to help you do a  cash for keys plan and pay the tenants to leave now ?

If they tell you they won't protect you against those things, then consider banning them.It's a sad world where we tell families they can't let their kids experience simple pleasures and get some exercise.

I can't believe we haven't considered this for our existing rental property.I'm curious, in the event that there was tenant induced damages to either their own property or landlord's real property, what would the recourse be if no renters insurance was in place?  

For most of us, it's a math exercise.