This question refers to the date that your mortgage company paid your annual property tax bill to the local tax authority, not when you made escrow payments. This date is usually in the last quarter of the year (e.g. Oct, Nov, Dec) and sometimes twice a year.
The annual mortgage account statement from the lender will usually list the date (or dates) paid, and the amount(s). The Form 1098-INT also lists the total amount paid. You can enter 12/31/2016 if unsure.