All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Part of the etiquette of Islam is to preserve and respect the Quran; this is part of the enjoined honoring of the ordinances of Allah, the Exalted. He says (what means): {whoever honors the sacred ordinances of Allah - it is best for him in the sight of his Lord.} [Quran 22:30] An aspect of the enjoined honoring of the Quran is to clean it from dust. The research papers of the Council of Senior Scholars quoted the following passage from Tanbeeh Al-Ghaafileen (book):
"Ahmad ibn Ibraaheem Ad-Dimashqi, said, 'Chapter on some of the religious innovations seen in mosques ... some mosques have Quranic verses written on the walls. According to our school (of Fiqh), this is disliked because it exposes the Quranic verses to dust. Al-Haleemi underlined in his book Al-Minhaaj that the due respect and glorification of Allah and His Messenger, sallallaahu ‘alayhi wa sallam, entail wiping away the dust from the Quran and Sunnah books and putting nothing of the household items on them. It is also disliked to write the Quran on any walls apart from the mosque. If it is on a wall that one climbs over to reach an upper room or the like, the dislike is more stressed and it may even be deemed prohibited." [Tanbeeh Al-Ghaafileen]
Therefore, the dear questioner and all Muslims should respect the Quran and clean it from dust to the best of their abilities. If he fails to do so, then he most likely bears no sin for it because it was not his fault. Moreover, it is difficult to avoid dust, and it is not regarded as filthy in and of itself. In addition, dust normally piles up on books. It would have been very difficult had it been obligatory on the Muslim to clean them from dust whenever he sees it and that he would bear a sin otherwise. If the person bears no sin in this situation, then he is not a disbeliever with greater reason.
For more benefit, please refer to fatwa 91638.
Allah knows best.