Returned deposit then discovered vermin

[Jackson Long]

About 8 months into the tenancy they informed they had a mouse problem, but that they were taking care of it.  I told them that if the house was vermin free at move-in it is their responsibility to handle it.  I had a good relationship with the tenant so when they moved out and said it was fixed I didn't dig into it.

New tenant immediately found mice (2 weeks after original tenant vacated) and I've hired an exterminator.  Exterminator says there is a ton of mouse traffic and is doing whatever program they sold me.

Am I entitled to, and should I even, request the tenant pay these costs?