How is the $125K "home acquisition indebtedness"?  The deceased father is the one who took out the mortgage, right?  Are you saying that just because they inherited the house, they inherited the characteristic of the mortgage being related to home acquisition?  What else did they inherit -- any cash?  Did Dad leave them $500K and they decided not to pay off his mortgage?  Is their basis less than the $125K, anyway?  Not that it might not make any difference.  

Why are you just getting around to asking now?  They did call you last year before they did this, right?

Here is the round hole of Code Section 163(h).  Try to pound your square peg into it:

(B)Acquisition indebtedness
(i)In general
The term “acquisition indebtedness” means any indebtedness which—
(I)is incurred in acquiring, constructing, or substantially improving any qualified residence of the taxpayer, and
(II)is secured by such residence.
 Such term also includes any indebtedness secured by such residence resulting from the refinancing of indebtedness meeting the requirements of the preceding sentence (or this sentence); but only to the extent the amount of the indebtedness resulting from such refinancing does not exceed the amount of the refinanced indebtedness.