What scripture do you have in mind? Where does Jesus provide a scenario where a woman may divorce a man and remarry or that the man who marries her is guilt-free?
The Old Testament did not allow women to divorce men, but a man was required to give a wife (or concubine in that passage) food clothing and sex. I read that the authorities in Jewish communities could try to pressure a man who wasn't living up to his duties to issue the bill of divorcement.
Matthew 19, Mark 10, etc. must have been a surprising scenario for the disciples. Shammai Pharisees were strict about divorce, and Hillel Pharisees were looser about it... but to use the word for adultery to describe divorce and remarriage was probably shocking and got the response 'If such be the case with the man and his wife it is better for a man not to marry.'
The Pharisees treated part of the Deuteronomy 24 passage like a command. Jesus responded that Moses because of the hardness of their hearts allowed divorce.
I wonder if that is what the NIV is trying to capture in the way it renders Deuteronomy 24.
Deuteronomy 24
24 If a man marries a woman who becomes displeasing to him because he finds something indecent about her, and he writes her a certificate of divorce, gives it to her and sends her from his house, 2 and if after she leaves his house she becomes the wife of another man, 3 and her second husband dislikes her and writes her a certificate of divorce, gives it to her and sends her from his house, or if he dies, 4 then her first husband, who divorced her, is not allowed to marry her again after she has been defiled. That would be detestable in the eyes of the Lord. Do not bring sin upon the land the Lord your God is giving you as an inheritance.
(NIV)
Under these conditions, the first husband is commanded not to marry her again after she has been defiled. The Pharisees were treating the giving of the marriage certificate as a command. Hillel Pharisees focused on 'displeasing', and following Hillel, included burning the meal as a reason. The Shammai Pharisees focused on 'something indecent' and would allow divorce for adultery or some other grave offense along those lines.
The Lord's teachings were more similar, IMO, to Shammai's on this particular topic, but the Lord Jesus used the word 'adultery.'