I think that if a parent asks that question of you, the first date for sure answer truthfully and do what you told them you would. After that date, maybe call either the shadchan/one of her references to make a further inquiry about the parents if you are still sincerely interested in the girl.
They could be very nervous themselves about their daughter dating. My mom has freaked out on multiple occasions because she knows I have spoken to many shadchanim over the past year and have not gotten a single in person date- her worry was that some people have been saying things about me that guys would ask as references and that the result was that I kept on getting “no”.