Taking over existing lease in NC

[Joseph Torres]

I'm currently in the middle of closing on a quad-plex in Burlington, NC. Every unit is currently rented for the next year, which is a good thing. I have all of the leases and everything looks good. I just did final walk thru yesterday and noticed that a tenant has cats which is not part of the lease agreement. The existing owner has asked that they remove the pets but I have a feeling they will not. My question is this. I know that I have to honor the existing lease which I'm fine with but can I make an amendment and require them to give me a non-refundable pet deposit and additional money per on the rent? Or, I have to hope this person actually removes the pets per the discussion with previous owner. 

I don't love the idea of pets because they can cause damage but I would be OK with a cat especially if they already had it before I took over ownership. I have another duplex that purchased 6 months ago but I was able to hand pick those tenants and selected those with no pets. 

Not entirely sure on my options.