Be that as it may, the report has a supporting mursal corroboration with a similar wording, transmitted by Ibn Abī Dāwūd, as cited in Fatḥ, and on the strength of this parallel chain it is ḥasan, God Most High willing; Ibn Khuzaymah even judged it ṣaḥīḥ.
I later retracted that assessment and concluded that the ḥadīth is weak; see Ḍaʿīf Abī Dāwūd (no. 71).
(Note) Al-Mundhirī (1/119 and 212–213) also attributed the ḥadīth to Ibn Mājah, but I believe he slipped, for I have not found it in Ibn Mājah’s Sunan, nor did any of the authorities whose sourcing I checked—as al-Ḥāfiẓ in Fatḥ (1), Abū al-Barakāt in al-Muntaqā, or al-Suyūṭī in al-Jāmiʿ—trace it to him. Likewise, al-Nāblusī, in al-Dhakhāʾir (1/46), cited it only to Abū Dāwūd.
His phrase “al-qadhāh,” pronounced with a light, dotted dhāl and a short vowel, denotes a single piece of chaff, dust, and the like. Linguists say that al-qadhā originally refers to something that falls into the eye or into a drink, and by extension to anything minor that may fall in the house or elsewhere.
Ibn Ruslān said in Sharḥ al-Sunan: “This ḥadīth encourages cleaning the mosques of even small bits of refuse, for such acts are recorded among one’s rewards and presented to one’s Prophet. If so small a deed is written down and presented, then greater deeds are even more certain to be recorded and displayed. Thus the text draws attention from the lesser to the greater, from what is pure to what is impure; and the reward for good deeds is proportionate to the act itself.” He said: