Early termination agreement

[Chas Sargent]

I purchased a duplex about a month and a half ago. One of the exiting tenants (2 males) found bed bugs and we have had a disagreement about who is responsible. Finally, I agreed to remedy the situation if the tenants would sign an addendum saying they acknowledge I am doing so and they are responsible for any future issues. I also told them if they didn't sign I would remedy and that they are free to leave.  

Now, they say they are moving out. My question is should I have (or attempt to have) them sign something like an early termination agreement? Anything else I should be aware of?