Hare Krsna-below we have a few instructions by Srila Prabhupada where he explains the rules of what and how to offer food to the Lord, who Krsna will accept this food from and who He wont accept it from. These are important guidlines which we should follow.
Hare Krsna
damaghosa das
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Devotees must be careful about eating food not offered to Lord Narayana or cooked by non devotees for their own sense gratification
Krsna book ch 58-“The Lord can be pleased only by a humble attitude in the service spirit. The more we render service unto the Lord under the direction of the spiritual master, the more we make advancement on the path approaching the Lord. We cannot demand any grace or mercy from the Lord because of our service rendered to Him. He may accept or not accept our service, but the only means to satisfy the Lord is through the service attitude, and nothing else.” 

Dec 13 1973LA—You can worship Kṛṣṇa anywhere, but you have to learn how to worship. What is that learning? Bhaktyā, that is the method. Therefore Kṛṣṇa says patraṁ puṣpaṁ phalaṁ toyaṁ yo me bhaktyāprayacchati [Bg. 9.26]. This patraṁ puṣpam is not important thing. The important thing is bhakti, devotion. That is wanted. Without bhakti, if you offer Kṛṣṇa very big plate, Kṛṣṇa is not hungry to take your food. He’ll not accept it. He’ll not accept anything if you do not offer with your love, bhaktyā, love and serving spirit: “My dear Kṛṣṇa, You are so opulent. I have nothing to offer You because You have got everything. But I have tried to collect the things to my best power, so I am offering You. Kindly take it.” This is mantra. This is mantra. Don’t require much mantra. That meekness, that humbleness, “Kṛṣṇa, I am most insignificant. I have nothing to give You, …Vidura invited Him, and Kṛṣṇa did not to go Arjuna’s house…, I mean to say, Duryodhana’s house, very palatial building. Vidura, a cottage, so He went there. And Vidura being in ecstasy was offering Him some banana. So he was so overpowered by ecstasy that instead of giving the fruit banana, he was giving the skin, and Kṛṣṇa was eating. So when he came to his senses he saw that “I have given only the skin, and Kṛṣṇa is eating.” So this is bhakti. This is bhakti. Kṛṣṇa wants that. Kṛṣṇa can eat anything, either you give the pulp or skin, He can eat anything because He is all powerful and everything is equal to Him.
Madhya 9.53–purportThe word apavitra anna refers to food that is unacceptable for a Vaiṣṇava. In other words, a Vaiṣṇava cannot accept any food offered by an avaiṣṇava in the name of mahā-prasāda. This should be a principle for all Vaiṣṇavas. When asked, “What is the behavior of a Vaiṣṇava?” Śrī Caitanya Mahāprabhu replied, “A Vaiṣṇava must avoid the company of an avaiṣṇava [asat].” The word asat refers to an avaiṣṇava, that is, one who is not a Vaiṣṇava. Asat-saṅga-tyāga,-ei vaiṣṇava-ācāra (Cc. Madhya 22.87). A Vaiṣṇava must be very strict in this respect and should not at all cooperate with an avaiṣṇava. If an avaiṣṇava offers food in the name of mahā-prasāda, it should not be accepted. Such food cannot be prasāda because an avaiṣṇava cannot offer anything to the LordSometimes preachers in the Kṛṣṇa consciousness movement have to accept food in a home where the householder is an avaiṣṇava; however, if this food is offered to the Deity, it can be taken. Ordinary food cooked by an avaiṣṇava should not be accepted by a Vaiṣṇava. Even if an avaiṣṇava cooks food without fault, he cannot offer it to Lord Viṣṇu, and it cannot be accepted as mahā-prasāda.
LA June 14 1972-lecture-He is mentioning especially vegetables, grains, fruits. But not that everyone can offer Kṛṣṇa all these things. No. He says yo me bhaktyā prayacchati. He does not accept anything from the hands of a nondevotee. Therefore the non-initiated student cannot offer Him.
He doesn’t accept. He says especially yo me bhaktyā prayacchati. He must be devotee. … Kṛṣṇa is giving you chance. It is very difficult to approach Kṛṣṇa, but Kṛṣṇa is so kind that He has appeared in your temple and He is accepting.
According to the rules and regulation, if you offer, He will accept.
This is the process of Deity worship.
Jan 26 1973 Calcutta–In every house of a brāhmaṇa there was Nārāyaṇa-śilā. Still some rigid brāhmaṇas, they worship. So Caitanya Mahāprabhu even, He did not accept prasādam from a non-Vaiṣṇava brāhmaṇa. He must be brāhmaṇa, at the same time, Vaiṣṇava. Then He would accept.So this regulation we should follow. We should not accept food, (only) prasādam. If anyone wants to give us food, then he must arrange for cooking food and offering to the Nārāyaṇa, to the Viṣṇu, Kṛṣṇa. Then we can take. This is the… Otherwise we… Bhuñjate te aghaṁ pāpā ye pacanty ātmā… People who are cooking for eating oneself, that cooking, that eating is simply sinful. Without prasādam, whatever we eat, that is, we are eating sin, That’s all. Therefore we must sufferWe should be careful. Bhuñjate te aghaṁ pāpā. This is parātma-niṣṭhā, that we should not accept anything which is not offered to Viṣṇu, or Kṛṣṇa.
May 6 1973 LA–.” Kṛṣṇa is not hungry. Kṛṣṇa is not hungry. He is self-satisfied, pūrṇa. But if His devotee offers Him something with love and affection, then He accepts. So do not think that “We have made such nice, sumptuous plate for Kṛṣṇa. Kṛṣṇa must eat.” No. There is no such thing, “must.” You cannot make Kṛṣṇa must. That is not possible. So Kṛṣṇa will see how much you have love for Him. Then He will accept. Otherwise He’ll reject. Therefore, it is forbidden, those who are nondevotee, those who are not initiated, those who are not chanting regularly, their offering to Kṛṣṇa will not be accepted. We must be very careful. We must know our position, whether I am sincerely following the principles of devotional service. Then Kṛṣṇa will accept. Yo me bhaktyā prayacchati. The real thing is bhakti. So either you offer Kṛṣṇa prayers or you offer foodstuff, everything must be along with bhakti, devotion, love. Then Kṛṣṇa will accept.
“Kṛṣṇa becomes obliged to the loving spirit of the devotee and not exactly to the service rendered.No one can serve Kṛṣṇa completely. He is so complete and self-sufficient that He has no need of any service from the devotee. It is the devotee’s attitude of love and affection for Kṛṣṇa that makes Him obliged.” (Nectar of Devotion, Chapter 40)