Contradiction with Leviticus 6:3-5
While Exodus 22:13 establishes restitution upon admission of an animal's death, Leviticus 6:3-5 specifies restitution only when the theft is voluntarily admitted rather than for accidental loss.
Leviticus 6:3-5: Or have found that which was lost, and lieth concerning it, and sweareth falsely; in any of all these that a man doeth, sinning therein:
Contradiction with Luke 19:8-9
In Exodus 22:13 restitution is for loss while here restitution is made voluntarily and beyond requirement for extortion.
Luke 19:8-9: And Zacchaeus stood, and said unto the Lord; Behold, Lord, the half of my goods I give to the poor; and if I have taken any thing from any man by false accusation, I restore [him] fourfold.
Contradiction with Matthew 5:40-42
Exodus 22:13 requires precise repayment for loss, whereas this text encourages giving beyond what is legally required.
Matthew 5:40-42: And if any man will sue thee at the law, and take away thy coat, let him have [thy] cloke also.
Paradox #1
The moral conflict in Exodus 22:13 could be seen in the responsibility and trust issues between the owner and guardian of the animal. There might be a tension between proving honesty in the situation versus the expectation of compensation or trust. This might lead to disputes over the fairness of determining what is truthful without solid evidence.