Note that the Wikipedia dates the close of the Talmud before Mohammed lived. Thus, it would have no reference to the incident that you are asking about.
The Talmud has two components: the Mishnah (Hebrew: משנה, c. 200 CE), a written compendium of Rabbinic Judaism's Oral Torah (Talmud translates literally as "instruction" in Hebrew); and the Gemara (c. 500 CE)
The period of Muhammad in Medina started with the Hijra (migration to Medina) in 622 and ended with the conquest of Mecca in 630.
The Jewish Virtual Library has an article about Jews in Arabia but it does not reference the Talmud at all.
Once the Moslems conquered there territories, there would have been influences during the gaonic period, but that also is not an answer to the question as written.