What is the ruling on distributing da'wah pamphlets that contain Qur'anic verses to non-Muslims, knowing that they may be thrown in the trash, and is it permissible to give them these pamphlets when they are not in a state of ritual purity?

Distributing da'wah (proselytizing) pamphlets and brochures that contain Quranic verses is permissible for a disbeliever and for one who is in a state of minor ritual impurity (muhdith) to touch, because they are not a Mushaf (a complete copy of the Quran), and the Quranic verses within them are mixed with other text. Therefore, there is no objection to distributing them and allowing a disbeliever to touch and read them, due to the benefit therein for calling people to Islam, and this benefit outweighs the harm of allowing them to touch it.

As for discarding these brochures in the trash, it is impermissible and forbidden for the one who performs the act. The publisher bears no responsibility. It is recommended to advise against discarding them in a disrespectful place.