What should we do with the small pieces that fall off the covers of old Qurans when reading them, and is it permissible to throw them in the trash?

These small detached pieces falling from the leaves or cover of the Mushaf (definition) do not have the ruling of the Mushaf. Their ruling depends on their content. If they are blank, they have the ruling of ordinary paper. However, if they contain a word deemed sacred by Islamic law, such as one of Allah's names or a Qur'anic verse, then it is not permissible to disrespect them. Nevertheless, they do not carry the ruling of the Mushaf regarding touching by one in a state of ritual impurity (hadath (definition)) and similar matters.