The Hadeeth regarding the revelation of this Surah where in Quraysh was asked to enquire from the Prophet (ﷺ) regarding three questions if he answered he is the true prophet otherwise not; You quoted it as inauthentic but it is quoted in Tafseer ibn Katheer as well as by Sheikh Al-Uthamyeen. If it is daeef they are using it for Dawah purpose and it is a solid point for calling non-Muslims. Can we still use it for Dawah purposes?

We have enough authentic Ahadeeth for Dawah purposes. We don’t need to go with the uncertain narrations and we shouldn’t feel it a problem to replace an inauthentic story with a certain one. It is true that some stories are very touching, it may bring tears to the eyes but the authenticity of the material should be taken care of.