Śrīmad-Bhāgavatam 10.41.13
Blended reading (Sanskrit + English inline)
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pāda-rajasā
—
with the dust of Your feet
Compound instrumental: pāda (foot) + rajas (dust). The most precious purifier in Vaiṣṇava idiom. Gauḍīyas hold pāda-padma-rajaḥ above all tīrtha-jala — Ganges-water is itself sanctified by having washed those feet (next verse).
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gṛha-medhinām
—
who are attached to household ritual duties
Compound: gṛha (house) + medhin (sacrificer). The technical term for the gṛhastha bound to the five mahā-yajñas. Akrūra labels himself thus with humility — admitting he has not transcended karma-kāṇḍa, and so begs the higher purification.
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punīhi
—
please purify
Imperative of √pū. The verb of yajña-suddhi. Akrūra inverts the ritual order: instead of a brāhmaṇa purifying the home by mantra, he asks the Supreme Person to purify it by His feet. Bhakti-yajña outranks vidhi-yajña.
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pitaraḥ
—
forefathers
Nominative plural of pitṛ. The ancestors fed by śrāddha. Their satisfaction depends not on rice-pinda but on the descendant's contact with Bhagavān. Gauḍīyas cite this verse as proof that one Vaiṣṇava in a family liberates fourteen generations.
"The water from washing the dust from your feet (yat saucena), which will fall in my house and on my head, will satisfy all the devas, agni and the pitras."
“Your houses will be protected by worship of the Pitṛs, the fire and the devatās.” Purify our houses with the dust from your feet. We are householders, constant engaged in harming others in five ways (by fire, sweeping, crushing, drowning and grinding). By purifying just once, they will all be continually satisfied (anutṛpyanti). By satisfying the Pitṛs and devatās, our household duties will be completed. Thus the houses will be successful.
A householder asks the king's elephant to step into his courtyard — knowing the footprint will sanctify the soil for generations. Akrūra knows that pādo-raja, not silver or cooked food, is the gift his pitṛs are actually waiting for.
In SB 1.8 Kunti laments Kṛṣṇa's departure from Hastināpura by saying that the road on which the dust of His feet lay was now empty. The Pāṇḍava queen, a kṣatriya woman, behaved exactly like Akrūra here: she measured holiness by the proximity of those feet.
Gauḍīyas read both verses together — pāda-rajaḥ-snāna is the highest sacrament. Caitanya Mahāprabhu's washing of Sārvabhauma Bhaṭṭācārya's house with the dust of His own feet (Caitanya-caritāmṛta) is the same līlā extended into Kali-yuga.
My note
Source: vedabase.io