Firstly, my condolences to you.
I don't understand the terminology that they seem to have used!
If you were given this over the telephone I would not rely on it as meaning that nothing is due. My inclination would be to put the same query to them in writing. If they confirm the position to be that nothing is owed well and good. I would make the enquiry in a very simple way i.e. don't go looking for trouble !
I think it is important to get this straightened out for purposes of probate, tax and even selling the property if that is intended. Hence the importance of getting the position officially clarified in writing.
Side bar point - if you have made payments of some elements of your mother's care check to see if you are owed any tax refund.