Two things I see in common in term of guilt offering between the old and new testament.
Confession of our sin is essential to bring forth healing
When anyone is guilty in any of these ways, he must confess in what way he has sinned and, as a penalty for the sin he has committed, he must bring to the Lord a female lamb or goat from the flock as a sin offering; and the priest shall make atonement for him for his sin.
James 5:16 New Living Translation (©2007)
Confess your sins to each other and pray for each other so that you may be healed. The earnest prayer of a righteous person has great power and produces wonderful results.
For the believer, our guilt offering is Jesus Christ. Restitution is our responsibility, and confession and cleansing are offered to us. Even if it is a recurring sin, we need to confess it and leave the guilt behind us.
The Guilt Offering