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I don't know why you offered them more time rent free! You gave them three months notice. If your state requires a grace period for late rent, you've just clouded the situation by telling them that they could stay rent free for more time. Now they could argue that the clock doesn't start on late rent until January 10th!
Sounds like you need to learn about rentals in NC. Like when you can padlock, when the tenants can come back in to get their possessions and how long they are allowed to take. Etc etc otherwise the tenants will take advantage of you. There are laws for all these things and you don't need to worry about being nice about it.