The ASQ-3 scores are domain scores; there are only 6 questions for each ASQ-3 area so skipping even 1 question
s means missing 1/6th (16.67%) of the data; omitting 2 items for an area means missing 2/6th or 33.33% of the data. There is only one ASQ:SE-2 score which is calculated from all of the items on a questionnaire (16 to 36 questions depending on the age interval). Skipping 2 items on an ASQ:SE-2 questionnaire results in missing a smaller portion of the data (e.g., 2 of 16 questions or 12.5% for the 2 month interval and 2 of 36 questions or 5.6% for the 60 month interval).
Also, ASQ:SE-2 cutoff points are calculated based on medians and interquartile ranges, which is very different from the means and standard deviations used to calculate ASQ-3 cut-off scores. The developers conducted analyses that confirmed that a child's classifications (below cutoff, monitoring zone, above cutoff) would not be significantly altered if 1 or 2 items were omitted on ASQ:SE-2. When 3 items are omitted and the score is within 5 points of the cutoff (above or below), you do need to calculate an adjusted score because a child's classification may be altered (moving from monitoring zone to above the cutoff, for example).
Of course, even if the scores do not need to be adjusted on ASQ:SE-2, it is always better to go back and ask parents to answer omitted items. It is possible they inadvertently skipped an item or need some additional explanation to answer it.