Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
One is not allowed to touch or carry al-Qur'an, if he is impure, partially or wholly (i.e. without Wudu or ceremonically impure), but this is not the case concerning the recorded Qur'anic materials. However, one is strongly advised to honor such recorded matters, i.e. to avoid entering a toilet while carrying such materials unless one fears losing them.
Allah knows best.