BhG 3.13

syntax

yajña-siṣṭāśinaḥ (those who eat the remnants of sacrifice) santaḥ (saints) sarva-kilbiṣaiḥ (from all sins) mucyante (they are released),
ye tu (but those who) ātma-kāraṇāt (for the own sake) pacanti (they cook),
te (these) pāpāḥ (sinners) agham (evil) bhuñjate (they eat).

grammar

yajña-śiṣṭāśinaḥ	–	yajña-śiṣṭa-āśin 1n.3 m.; TP: yajñasya śiṣṭāni āsina iti – those who eat the remnants of sacrifice (from: √yaj – to consecrate, to sacrifice, to worship, yajña – sacrifice, worship, name of Viṣṇu; √śiṣ – to leave, PP śiṣṭa – left, remnants; √aś – to reach, to eat, to enjoy, āśin – one who eats, enjoys; -in, -min, -vin – sufixes meaning one who possesses);
santaḥ	–	sant (√as – to be) PPr 1n.3 m. – being, true, existing, saints;
mucyante	–	√muc (to liberate, to release) Praes. pass. 1v.3 – they are released (from what? – pass. requires instrumental or ablative);
sarva-kilbiṣaiḥ	–	sarva-kilbiṣa 3n.3 n.; sarvair kilbiṣaiṛ iti – from all sins (from: sarva – all, whole; kilbiṣa – fault, offence, sin);
bhuñjate	–	√bhuj (to eat, to enjoy) Praes. Ā 1v.3 – they eat;
te	–	tat sn. 1n.3 m. – they;
tu	–	av. – but, then, or, and;
agham	–	agha 2n.1 n. – evil, sin, suffering;
pāpāḥ	–	pāpa 1n.3 m. – sinners, wicked people;
ye	–	yat sn. 1n.3 m. – those who;
pacanti	–	√pac (to cook, to digest) Praes. P 1v.3 – they cook;
ātma-kāraṇāt	–	ātma-kāraṇa 5n.1 n.; TP: ātmanaḥ kāranāt iti – from the cause of one’s self, for the own sake (from: ātman – self; √kṛ – to do, karaṇa – deed, direct cause, instrument, helper, kāraṇa – cause, motive, principle, the means);

textual variants

yajña-siṣṭāśinaḥ → yajña-siṣṭāśanaḥ (those who have as food the remnants of the sacrifice);
sarva-kilbiṣaiḥ → te ‘pi kilbiṣaiḥ (they even from sins);
bhuñjate te tv aghaṁ pāpā → te tv aghaṁ bhuṁjate pāpā (but those sinners eat sin);

Śāṃkara

The key:
an excerpt from the commented verse
quotes from the scriptures
starting polemic

On the other hand,		ye punaḥ –
The righteous, who eat the remnant of the sacrifice, are freed from all sins; but sin do the impious eat who cook for their own sakes.		yajña-śiṣṭāśinaḥ santo mucyante sarva-kilbiṣaiḥ | bhuñjate te tv aghaṃ pāpā ye pacanty ātma-kāraṇāt ||3.13||
Those who, after performing sacrifices to the Gods, &c., eat the remains of the food – which is called amṛta, ambrosia – are freed from all sins committed at the five places of animal-slaughter (such as the fire-place), as well as from those sins which result from involuntary acts of injury and other causes.		deva-yajñādīn nirvartya tac-chiṣṭam aśanam amṛtākhyam aśituṃ śīlaṃ yeṣāṃ te yajña-śiṣṭāśinaḥ santo mucyante sarva-kilbiṣaiḥ sarva-pāpaiś culiy-ādi-pañca-sūnā-kṛtaiḥ pramāda-kṛta-hiṃsādi-janitaiś cānyaiḥ |
But as to the others, who are selfish and cook food for their own sakes, what they eat is sin itself, while they themselves are sinners.		ye tv ātmaṃbharayo bhuñjate te tv aghaṃ pāpaṃ svayam api pāpā ye pacanti pākaṃ nirvartayanti ātma-kāraṇāt ātma-hetoḥ ||3.13||

Rāmānuja

tad eva vivṛṇoti

indrādyātmanāvasthitaparamapuruṣārādhanārthatayaiva dravyāṇy upādāya vipacya tair yathāvasthitaṃ paramapuruṣam ārādhya tacchiṣṭāśanena ye śarīrayātrāṃ kurvate, te tv anādikālopārjitaiḥ kilbiṣaiḥ ātmayāthātmyāvalokanavirodhibhiḥ sarvair mucyante / ye tu paramapuruṣeṇendrādyātmanā svārādhanāya dattāni ātmārthatyopādāya vipacyāśnanti, te pāpātmano ‚gham eva bhuñjate / aghapariṇāmitvād agham ity ucyate / ātmāvalokanavimukhāḥ narakāyaiva pacante

Śrīdhara

ataś ca yajanta eva śreṣṭhāḥ | netara ity āha yajña-śiṣṭāśina iti | vaiśva-devādi-yajñāvaśiṣṭaṃ ye ‚śnanti te pañcasūnākṛtaiḥ sarvaiḥ kilbiṣair mucyante | pañca-sūnāś ca smṛtāv uktāḥ –

kaṇḍanī peṣaṇī cullī udakumbhī ca mārjanī |
pañca-sūnā gṛhasthasya tābhiḥ svargaṃ na vindati || iti ||

ye ātmano bhojanārtham eva pacanti, na tu vaiśvadevādy-arthaṃ te pāpā durācārā agham eva bhuñjate

Madhusūdana

ye tu vaiśvadevādi-yajñāvaśiṣṭam amṛtaṃ ye ‚śnanti te santaḥ śiṣṭā vedokta-kāritvena devādy-ṛṇāpākaraṇāt atas te mucyante sarvair vihitākaraṇa-nimittaiḥ pūrva-kṛtaiś ca pañca-sūnā-nimittaiḥ kilbiṣaiḥ | bhūta-bhāvi-pātakā-saṃsargiṇas te bhavantīty arthaḥ |

evam anvaye bhūta-bhāvi-pāpābhāvām uktvā vyatireke doṣam āha bhuñjate te vaiśvadevādy-akāriṇo ‚ghaṃ pāpam eva | tu-śabdo ‚vadhāraṇe | ye pāpāḥ pañca-sūnā-nimittaṃ pramāda-kṛta-hiṃsā-nimittaṃ ca kṛta-pāpāḥ santa ātma-kāraṇād eva pacanti na tu vaiśvadevādy-artham | tathā ca pāñca-sūnādi-kṛta-pāpe vidyamāna eva vaiśvadevādi-nitya-karmākaraṇa-nimittam aparaṃ pāpam āpnuvantīti bhuñjate te tv aghaṃ pāpā ity uktam | tathā ca smṛtiḥ –

kaṇḍanī peṣaṇī cullī udakumbhī ca mārjanī |
pañca-sūnā gṛhasthasya tābhiḥ svargaṃ na vindati ||iti |

pañca-sūnākṛtaṃ pāpaṃ pañca-yajñair vyapohati iti ca | śrutiś ca idam evāsya tat-sādhāraṇam annaṃ yad idam adyate | sa ya etad upāste na sa pāpnamo vyāvartate miśraṃ hy etat iti | mantra-varṇo ‚pi –

mogham annaṃ vindate agra-cetāḥ
satyaṃ bravīmi vadha itsa tasya |
nāryamāṇaṃ puṣyati no sakhāyaṃ
kevalādho bhavati kevalādī ||iti |

idaṃ copalakṣaṇaṃ pañca-mahā-yajñānāṃ smārtānāṃ śrautānāṃ ca nitya-karmaṇām | adhikṛtena nityāni karmāṇy avaśyam anuṣṭheyānīti prajāpati-vacanārthaḥ

Viśvanātha

vaiśvadevādi-yajñāvaśiṣṭam annaṃ ye ‚śnanti te pañca-sūnākṛtaiḥ sarvaiḥ pāpair mucyante | pañca-sūnāś ca smṛty-uktāḥ –

kaṇḍanī peṣaṇī cullī udakumbhī ca mārjanī |
pañca-sūnā gṛhasthasya tābhiḥ svargaṃ na vindati || iti

Baladeva

ye indrādy-aṅgatayāvasthitaṃ yajñaṃ sarveśvaraṃ viṣṇum abhyarcya tac-cheṣam aśnanti tena tad-deha-yātrāṃ sampādayanti te santaḥ sarveśvarasya yajña-puruṣasya bhaktāḥ sarva-kilbiṣair anādi-kāla-vivṛddhair ātmānubhava-pratibandhakair nikhilaiḥ pāpair vimucyante | te tu pāpāḥ pāpa-grastāḥ agham eva bhuñjate | ye tat-tad-devatāṅgatayāvasthitena yajña-puruṣeṇa svārcanāya dattaṃ vrīhy-ādy-ātma-kāraṇāt pacanti tad vipacyātma-poṣaṇaṃ kurvantīty arthaḥ | pakvasya vrīhy-āder agha-rūpeṇa pariṇāmād aghatvam uktam