If alimony has been awarded it will not be reduced at this point merely because you chose to pay off the mortgage with your property settlement.
Just have to chime in…
GREAT that you want to pay off your mortgage. If you have ANY credit card debt or other debt, it would be in you best interest to pay THAT off instead of your mortgage in that the interest on those loans will probably be much more that your mortgage payment. PLUS you still benefit from mortgage interest deduction if you itemize your taxes. If you have any money left after paying off the other loans, then by all means put it toward the house ( or some toward a retirement plan)…more equity when and if you decide to sell (smile) and/or some retirement funds later.