I would never tell a lie
The town council I met last week asked for the number of cats that each caregiver was taking care of, so that they would know how many cats there were in each area.
One of the caregivers went around asking the others to collate the figures, and people starting under-reporting the numbers to her. This is really bad for two reasons.
(1) If the town council finds out, your credibility is shot;
(2) If there is a complaint, and they go to count, they'll tell you obviously sterilisation is not working, and that you're doing a bad job because the number increased.