The corresponding verses in Matthew 5 are:
23 Therefore if thou bring thy gift to the altar, and there rememberest that thy brother hath ought against thee;
24 Leave there thy gift before the altar, and go thy way; first be reconciled to thy brother, and then come and offer thy gift.
The 3 Nephi version leaves out references to bringing a gift to the altar. That “gift” was the sacrifice under the law of Moses. Since the New World situation is moving away from the context of the law of Moses, bringing a sacrifice as part of a petition to God was no longer applicable. Therefore, it was removed.
What becomes important in Jesus’s elaboration of the meaning of the law was that one’s heart be an appropriate sacrifice. Thus, if one came to the Lord burdened with conflicts with another, those earthly issues should be reconciled so that one could approach the Lord with a pure heart and a contrite spirit.