What is the ruling on the Qur'anic ختمة (recitation of the entire Quran) performed by some Muslims by individually reading parts of the Mushaf, then gathering for supplication and a feast?

Gathering to recite and study the Qur’an is among the best of deeds. As for the description mentioned in the question—distributing parts, silent reading, then supplication and a banquet—this is an invented method that was not transmitted from the Prophet, peace and blessings be upon him, nor from his companions. The Prophet, peace and blessings be upon him, said: "Whoever introduces into this matter of ours that which does not belong to it, it is to be rejected."