Assalamu alaikum wa rahmatullahi wa barakatuh,
Allah knows best but I have never come across a hadeeth which says the people will destroy the Quran with their hands at the end of time.
There are a number of ahadeeth which say that the Quran will be taken away. Among these ahadeeth are the following:
From Abdullah ibn Masood, who said:
“Something will come and take the Quran one night and not one ayah
will be left, either in the Mus'haf or in the heart of any person, but
it will be taken away.”
(Narrated by al-Darimi with a saheeh isnaad, no. 3209)
Imam Ad-Daarimi also narrated with a different saheeh isnaad (no. 3207) that Abdullah ibn Masood said:
“Recite the Quran much before it is taken away.” They said, “These
Mus'hafs will be taken away?! What about that which is (memorized) in
the hearts of men?” He said: “Something will come and take it one
night, and in the morning they will wake up without it. They will
forget the phrase ‘laa ilaha ill-Allah’ and they will start to recite
the sayings and poetry of the Jahiliyyah. That is when the Word will
be fulfilled against them.”
This is one of the tribulations that will happen at the end of time, concerning which our Prophet sallallahu alaihi wa sallam said:
"Hasten to do good deeds before tribulations come like patches of dark
night, when a man will wake up as a believer and by evening he will be
a kaafir, or in the evening he will be a believer and by morning he
will be a kafir, selling his religion for some worldly gains.”
(narrated by Muslim, no. 169).
And Allah knows best.
We ask Allah to make us adhere firmly to His religion and to protect us from tribulations, both seen and unseen.