Objection 1. It would seem that a husband could lawfully take back the wife he had divorced. For it is lawful to undo what was ill done. But for the husband to divorce his wife was ill done. Therefore it was lawful for him to undo it, by taking back his wife.
Objection 2. Further, it has always been lawful to be indulgent to the sinner, because this is a moral precept, which obtains in every law. Now the husband by taking back the wife he had divorced was indulgent to one who had sinned. Therefore this also was lawful.
Objection 3. Further, the reason given (Deuteronomy 24:4) for its being unlawful to take back a divorced wife was "because she is defiled." But the divorced wife is not defiled except by marrying another husband. Therefore at least it was lawful to take back a divorced wife before she married again.
On the contrary, It is said (Deuteronomy 24:4) that "the former husband cannot take her again," etc.
I answer that, In the law concerning the bill of divorce two things were permitted, namely for the husband to put away the wife, and for the divorced wife to take another husband; and two things were commanded, namely that the bill of divorce should be written, and secondly that the husband who divorced his wife could not take her back. According to those who hold the first opinion (3) this was done in punishment of the woman who married again, and that it was by this sin that she was defiled: but according to the others it was done that a husband might not be too ready to divorce his wife if he could nowise take her back afterwards.
Reply to Objection 1. In order to prevent the evil committed by a man in divorcing his wife, it was ordered that the husband could not take back his divorced wife, as stated above: and for this reason it was ordered by God.
Reply to Objection 2. It was always lawful to be indulgent to the sinner as regards the unkindly feelings of the heart, but not as regards the punishment appointed by God.
Reply to Objection 3. There are two opinions on this point. For some say that it was lawful for a divorced wife to be reconciled to her husband, unless she were joined in marriage to another husband. For then, on account of the adultery to which she had voluntarily yielded, it was assigned to her in punishment that she should not return to her former husband. Since, however, the law makes no distinction in its prohibition, others say that from the moment that she was put away she could not be taken back, even before marrying again, because the defilement must be understood not in reference to sin, but as explained above (4, ad 3).
Source: Summa Theologica (New Advent)