All of the offerings confront the believer with challenges in regard to how we may walk a holy and righteous life. Some of the shadows and examples are profitable and the New Testament develops many of these teachings.
To put things right and make peace with those offended is part of any offering. Clean hands and a pure heart is the result of such an action and God is well pleased.
(Mat 5:23-24 NRSV) So when you are offering your gift at the altar, if you remember that your brother or sister has something against you,  leave your gift there before the altar and go; first be reconciled to your brother or sister, and then come and offer your gift.
Things that are spoken have great power to harm and defile both the speakers and the hearers. Such trespass needs to be dealt with in our walk. There are steps to be taken.
i. go to the person alone. If they do not listen then:
ii. take one or two with you. If no response then:
iii tell it to the church. (wisdom would read this as Elders who represent the church and have the understanding to deal with such problems wisely)
(Mat 15:18 NRSV) But what comes out of the mouth proceeds from the heart, and this is what defiles.
(Mat 18:15 NRSV) “If another member of the church sins against you, go and point out the fault when the two of you are alone. If the member listens to you, you have regained that one.
(Mat 18:16-18 NRSV) But if you are not listened to, take one or two others along with you, so that every word may be confirmed by the evidence of two or three witnesses.  If the member refuses to listen to them, tell it to the church; and if the offender refuses to listen even to the church, let such a one be to you as a Gentile and a tax collector.
If any member of the church offends us we are likely to be confronted with the thought “How much longer must I put up with this?” Peter had a similar problem.
The reply he received really means forever. It links with the knowledge that only God may judge. An unforgiving heart is judgemental.
(Mat 18:21 NRSV) Then Peter came and said to him, “Lord, if another member of the church sins against me, how often should I forgive? As many as seven times?”
We all commit trespass
Jesus teaches that forgiveness is the answer. The Levitical offerings remind us of the necessity of priestly cleanliness before an offering.
(Mat 6:14-15 NRSV) For if you forgive others their trespasses, your heavenly Father will also forgive you;  but if you do not forgive others, neither will your Father forgive your trespasses.
Unforgiveness and prayer
As we pray before the Golden Altar there is good reason to be sure that we have forgiven all who have offended us. The furniture of the Outer Court stands as an example to us all. Deal with sin and wash in the Word of God that we may be fit to pray before the Veil.
(Mark 11:24-25 NRSV) So I tell you, whatever you ask for in prayer, believe that you have received it, and it will be yours.  “Whenever you stand praying, forgive, if you have anything against anyone; so that your Father in heaven may also forgive you your trespasses.”
The new and living way
All of the offerings and teachings of Leviticus have been written for an example to us and help to enlarge our understanding of our wonderful Lord. Remember however that they are shadows and types of the truth that was only fully revealed in our Lord Jesus Christ.
Whenever you read various attempts to explain these writings be careful to read the Scriptures for yourself in context and seek the aid of the Holy Spirit to quicken the Word to your understanding.
In particular be meticulous in separating the ideas that spring from the imagination and the “I think” of the writer. There are many places where comments such as “this means” is more correctly written “I think this means”. Such comment is not supported evidence but is often inspired guesswork.
(2 Cor 5:17-19 NIV) Therefore, if anyone is in Christ, he is a new creation; the old has gone, the new has come! All this is from God, who reconciled us to himself through Christ and gave us the ministry of reconciliation: that God was reconciling the world to himself in Christ, not counting men’s sins against them. And he has committed to us the message of reconciliation.
An interesting comment made by some writers is that the gospels tend to have characteristics similar to the Levitical Offerings.
Matthew: Trespass Offering.
Mark: Sin Offering.
Luke: Peace Offering.
John: Burnt Offering.
JESUS FULFILLED ALLTHE OFFERINGS OF LEVITICUS
(Mat 5:17 KJV) Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil.
(Eph 5:2 NRSV) and live in love, as Christ loved us and gave himself up for us, a fragrant offering and sacrifice to God.
(John 6:51 NRSV) I am the living bread that came down from heaven. Whoever eats of this bread will live forever; and the bread that I will give for the life of the world is my flesh.”
(John 12:24 NRSV) Very truly, I tell you, unless a grain of wheat falls into the earth and dies, it remains just a single grain; but if it dies, it bears much fruit.
(Rom 5:1 NRSV) Therefore, since we are justified by faith, we have peace with God through our Lord Jesus Christ.
(Col 1:20 NRSV) and through him God was pleased to reconcile to himself all things, whether on earth or in heaven, by making peace through the blood of his cross.
(Rom 8:3 NRSV) For God has done what the law, weakened by the flesh, could not do: by sending his own Son in the likeness of sinful flesh, and to deal with sin, he condemned sin in the flesh
(2 Cor 5:21 NRSV) For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God.
(Heb 13:11-12 NRSV) For the bodies of those animals whose blood is brought into the sanctuary by the high priest as a sacrifice for sin are burned outside the camp. Therefore Jesus also suffered outside the city gate in order to sanctify the people by his own blood.
(1 Cor 1:9 NRSV) God is faithful; by him you were called into the fellowship of his Son, Jesus Christ our Lord.
(2 Cor 5:19 NRSV) that is, in Christ God was reconciling the world to himself, not counting their trespasses against them, and entrusting the message of reconciliation to us.
(Col 2:13-14 NRSV) And when you were dead in trespasses and the uncircumcision of your flesh, God made you alive together with him, when he forgave us all our trespasses, erasing the record that stood against us with its legal demands. He set this aside, nailing it to the cross.