Clean the unit immediately.

If you want to do a background check and lease for Airbnb bookings, you have to put it in the house rules so you have the guest agree to do it after confirming the booking on Airbnb.We don't do mid stay cleanings, but we do expect a deeper clean after all our MTR stays.

I am guessing they do everything including cleaning themselves and must have paid all cash.  

I would see if you could clean the stove grate before replacing it.

Many national STR PM companies working on a percentage of gross income (Daily rates + cleaning fees) charge an elevated cleaning fee.

Also, landlord and tenant are guilty of violating their agreements with the Section 8 program.At this juncture, the landlord should use the security deposit for what it was intended for.... damages, extra cleaning, unpaid utilities, unpaid fees, unpaid rent.  

i cover pest control and lawn care on my stuff. keeps down on issues and i know the place looks good. for my student rentals i also build in a quarterly cleaning fee where my cleaning lady comes through and does a deep clean. extra eyes on stuff and parents happily pay it to ensure their kids have a solid spot. pass through cost for me and well worth it. 

The best run, most efficient and very clean city I have ever lived in and that includes places on 3 continents.

We do not want put ourselves at risk of paying off the tax lien and then not getting a clean title or worse yet, having the seller back out on us.I hope that makes sense and I really appreciate any advice.

Just clean it out and move on.