Deuteronomy 24:4

it shall not be in the power of the first husband who dismissed her at the beginning to return and take her to be with him as his wife, after that she hath been defiled; for that is an abomination before the Lord: for the children whom she might bear should not be made abominable, or the land which the Lord your God giveth you to inherit become obnoxious to the plague.

she became impure with respect to the first husband only. The sense is that she is impure to him , because she had sexual relations with another man. The ṭet acquires a dagesh because it absorbs the tav of the hotpa‘el. Compare, “the symptom after being laundered” [Leviticus 13: 55].

The command you must not defile is addressed to the nation of Israel.

[HER FORMER HUSBAND, WHO SENT HER AWAY, MAY NOT TAKE HER AGAIN TO BE HIS WIFE] AFTER THAT SHE IS DEFILED — “this includes a sotah (a suspected adulteress) who had been in seclusion [with a man against whom her husband had warned her not to seclude herself].” This is Rashi’s language. But the meaning thereof is that she had committed adultery while she was a married person, but in the case of a sotah who had merely been secluded and it is not known whether she was defiled — he [her husband] does not transgress this prohibition [if he continues to live with her]. It is so clearly explained in the first chapter of Tractate Yebamoth: “What is the meaning of v’nisterah?. She committed adultery. And why does Scripture refer to it as v’nisterah [which means, ‘but she was secluded’]? It is a more seemly expression.” On this answer the Gemara asked: “If she committed adultery — that [aspect] is clearly stated, and she hid and she be defiled,. [and therefore v’nisterah in the verse before us must have another meaning]! It is to declare that the husband [whose wife committed adultery and, as a result was divorced] transgresses a negative commandment [if he remarries her].” And if so, Scripture states here: “Her former husband, who sent her away, may not take her again to be his wife ‘and’ after that she is defiled [he may also not take her again].” Thus, these are two negative commandment: he warns against remarrying his own divorcee after she had married [someone else and was divorced or widowed], and he warns against remarrying his [former] wife who had been defiled by adultery [and divorced]. And in line with the plain meaning of Scripture the expression after that she is defiled refers to the first husband, the verse suggesting that because she “knew” [i.e., married] another man she is accounted to him [i.e., the first husband] as “defiled.”
Now these are newly-declared commandments both with respect to divorce and remarriage. And the reason for this prohibition is so that people should not exchange their wives with one another: he would be able to write her a bill of divorce at night, and in the morning she will return to him. This is the sense of the expression, and thou shalt not cause the Land to sin, for this is a cause of great sins. And in the Sifre it is stated: 270. “And thou shalt not cause the Land to sin — this is intended to admonish the court concerning this.”

כי תועבה היא, because this is a sure recipe leading to legalised adultery, people marrying for short periods of time, and then legally swapping wives by going through phony but legally correct divorce procedures.