If you do not have them removed and they get a refund from Airbnb, file charges against them for defrauding an innkeeper. 

Five years later, my (now ex) wife and I purchased a bed and breakfast that came with a second home for the Innkeepers (us) to live in.

The DA declined to prosecute her on charges of Defrauding an Innkeeper which, surprisingly, has quite a hefty fine attached.

Unless you are renting rooms in a home you also occupy, L-T rules apply - otherwise, most states allow boarders to come under "innkeeper" laws.

Okay, this is a spill over from the innkeepers rights.

As I am not an innkeeper by definition of law, I must refuse week-to-week tenancy."

Thanks @Wesley Williams for the intro@Jonathan Smith there's a lot you can do with just a little marketing.You could call the basement an "office" or a "den" and that's something you could market for higher rent.Also, I've written in detail about an "Inn Keeper" profit center where the landlord joint ventures with the tenant to host Airbnb/VRBO guests. 

But also give thought and study the fundamentals of being a virtual innkeeper.

Turn the "house" into a true Bed & Breakfast, and have an innkeeper I'd like to hire.

These brokers also act as consultants for current and want-to-be innkeepers by hosting seminars, providing "inn tune-up" one on one consulting, and speaking at conferences.