First, you should try to contact the parent and determine which response they intended to choose for that item. If you cannot get a response from the parent, you should drop that item from the scoring (similar to a parent skipping an item) and calculate an adjusted score.
Information about adjusted scoring is found in the ASQ:SE-2 User's Guide on page 92. For ASQ:SE-2 questionnaires, if there is just one or two items omitted (or dropped because of dual responses), you do not need to calculate an adjusted score. You can use the total score. Adjusted scores for ASQ:SE-2 only need to be calculated if 3 items are missing/omitted AND the score is within 5 points of a cutoff.