Case:


Ruling: The mishna (Sanhedrin 24a) cites a machloket whether one who accepts a relative or other invalid witness can back out of his agreement. However, the gemara explains that this is only when the ruling has already been handed down. On the other hand, if a kinyan was made to finalize the agreement, then the sides cannot back out (Shulchan Aruch, Choshen Mishpat 22:1).
The Shach points out that the Rishonim dispute why it is that the kinyan is binding and is not considered a kinyan devarim, an agreement on something too abstract to take effect (e.g., a future action). The Nimukei Yosef understands that the kinyan does not take effect on any object or monetary obligation but finalizes the parties’ agreement to be bound by the testimony. The Ra’avan, however, says that the kinyan obligates the parties to the monetary outcome of the testimony by conditionally creating a debt to pay or relinquishing rights to payment, respectively.
Beit din concluded that the Nimukei Yosef’s opinion, that the kinyan is not directly monetary in nature, is the more accepted one. The Rambam (Sanhedrin 7:2) uses the language of "accepted upon himself to be mochel" which sounds like a kinyan devarim that nevertheless works. Tosafot (Bava Metzia 74a) talks about accepting unfit witnesses "with words alone." In this case, since the wife signed a document before beit din binding her to accept her brother’s testimony, it should be valid, as a signed document is an effective form of kinyan.
However, there is a problem in accepting the permission for the relative to testify in this case. That is because such acceptance is able to work specifically regarding monetary cases, where a person can obligate himself in the money that is at stake. However, here the issue is whether or not the woman will be required to accept a get. The Terumat Hadeshen (173) says that a kinyan does not take effect regarding this matter. Therefore, it makes sense that acceptance of unfit witnesses will not be binding either.
It is true that the Rashbam (Bava Batra 128a) says that accepting unfit witnesses is not the acceptance of an obligation but the granting of credibility to the witnesses. According to that approach, it should work in regard to gittin as well. However, the rest of the Rishonim do not view it that way. Therefore, the wife can back out of her acceptance of her brother as a witness.