Other things to consider: what is your current debt/ interest rate/ appreciation... is it possible to refi and secure better cash flow?

Much more common is to have a mortgage (or in some states a deed of trust)  There is a promissory Note, which is the loan document and The mortgage is the document that gives the lender a security interest in the property. 

As you said, most banks expect it and some even require a special purpose entity be created for the purpose of holding the real estate securing the loan.

I would also add security cameras to document any additional damages.  

We had to take down a tree 2 weeks ago-a very large oak that split in half from its own weight.

I have 8 separate 5 yr fixed rate mortgages (and P.notes) that the same bank (in Wisconsin) has made to two of my LLC's and secured each loan on a separate property. 

This way if they do not pay, you can give them 30 days notice and take the security deposit to cover delinquent rent.   

We offered the full asking price but made sure that we have enough time to do our due diligence and secure financing.

Since they are on the hook until May, should I just use their security deposit to get house into renting shape?

Do I have any reason to return the security deposit / any defense if I choose not to?