3v.632 "One endowed with the triple knowledge,
Of proper birth, of ample learning,
Accomplished in knowledge and conduct,
Might partake of this milk-rice meal." [n.444] Spk: He speaks of one endowed "with the triple knowledge" (tīhi vijjāhi) with reference to the Three Vedas. By "proper birth" (jātima) he means one of pure birth through seven generations.

4v.633 "Even though one mutters many chants,
One does not become a brahmin by birth
If one is rotten within and defiled,
With followers gained by fraudulent means. sn.i.167

5v.634 "One who has known his past abodes,
Who sees heaven and the plane of woe,
Who has reached the destruction of birth,
A sage consummate in direct knowledge: [n.445] The Buddha’s reply refers to the tevijja of his own system of training: pāda a, to knowledge of the recollection of past abodes; pāda b, to the divine eye, i.e., the knowledge of the passing away and rebirth of beings; and pāda c, to the knowledge of the destruction of the taints.

6v.635 "By means of these three kinds of knowledge
One is a triple-knowledge brahmin.
This one accomplished in knowledge and conduct
Might partake of this milk-rice meal."

8v.636 "Food over which verses have been sung
Is not fit to be eaten by me.
This, brahmin, is not the principle
Observed by those who see.
The Enlightened Ones reject such food
Over which verses have been sung.
As such a principle exists, O brahmin,
This is their rule of conduct.

9v.637 "Serve with other food and drink
The consummate one, the great seer
With taints destroyed and remorse stilled,
For he is the field for one seeking merit." [n.446] Spk paraphrases the idea behind vv. 636–37 thus: "Though I stood for such a long time waiting for alms, you would not give me even a spoonful; but now, after I have revealed all the Buddha-qualities to you as though spreading out sesamum seeds on a mat, (you wish to give). This food has been gained, as it were, by chanting a song; therefore, because it has been ‘chanted over with verses’ (gāthābhigīta) it is not fit to be eaten by me. As such a principle exists (dhamme sati), out of regard for the Dhamma, established on the Dhamma, the Buddhas sustain their life. This is their rule of conduct; this is their way of livelihood (esa vutti ayaṁ ājīvo). Such food is to be discarded and only what is righteously gained is to be eaten."
The Buddha’s practice is discussed at Mil 228–32. CPD (s.v. abhigīta) suggests that the reason the Buddha rejects such food is because it has been "spoken over with mantras"—by the brahmin while chanting the sacrificial hymns—but to me it is doubtful the Buddha would reject food for such a reason. Further, according to MW, gatha is not used with reference to the verses of the Vedas, and thus here the word more likely refers to the Buddha’s own verses.
Spk does not comment on kevalinaṁ, "the consummate one," in pāda a, but Pj II 153,9–10 (to Sn 82) says: Kevalinan ti sabbaguṇaparipuṇṇaṁ sabbayogavisaṁyuttaṁ vā; "a consummate one is one complete in all excellent qualities or one detached from all bonds." Spk II 276, 32–277, 1 (to SN III 59,34) explains: Kevalino ti sakalino katasabbakiccā; "the consummate ones are entire, they have completed all their tasks." For a further selection of relevant passages, see GD, p. 161, n. to 82. For reflections on the implications of the term, see ñāṇananda, SN-Anth 2:100–1.
Spk explains kukkuccavūpasantaṁ thus: hatthakukkuccādīnaṁ vasena vūpasantakukkuccaṁ; "one in whom remorse has been stilled by the stilling of fidgety behaviour with the hands, etc." Here kukkucca is understood in the literal sense of "bad activity" or "fidgety behaviour" rather than in the extended sense of remorse or worry, one of the five hindrances.

3"Tīhi vijjāhi sampanno,
jātimā sutavā bahū;
Vijjācaraṇasampanno,
somaṁ bhuñjeyya pāyasan"ti.

4"Bahumpi palapaṁ jappaṁ,
na jaccā hoti brāhmaṇo;
Antokasambu saṅkiliṭṭho,
kuhanāparivārito.

5Pubbenivāsaṁ yo vedī,
saggāpāyañca passati;
Atho jātikkhayaṁ patto,
abhiññāvosito muni.

6Etāhi tīhi vijjāhi,
tevijjo hoti brāhmaṇo;
Vijjācaraṇasampanno,
somaṁ bhuñjeyya pāyasan"ti.

8"Gāthābhigītaṁ me abhojaneyyaṁ,
Sampassataṁ brāhmaṇa nesa dhammo;
Gāthābhigītaṁ panudanti buddhā,
Dhamme sati brāhmaṇa vuttiresā.

9Aññena ca kevalinaṁ mahesiṁ,
Khīṇāsavaṁ kukkuccavūpasantaṁ;
Annena pānena upaṭṭhahassu,
Khettañhi taṁ puññapekkhassa hotī"ti.