Is there any mention at all in the Talmud that backs the claim in the Quran that there were three Jewish tribes that lived in Medina at the time of Mohammad?
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 their territories, there would have been influences during the gaonic period, but that also is not an answer to the question as written. The Talmud and Islam talks about this, but starts with the yeshivos of Sura and Pumpedisa after the time of Mohammed and the conquest, which again does not deal with the question as asked.
As their links with the new metropolis strengthened, the luminaries of Sura and Pumbedita found they had much in common with their opposite numbers in the Islamic world.
That article refers to Gideon Libson in Halakhah and Reality in the Geonic Period.
According to S.D. Gottein's essay "Who were Muhammad's main teachers?" (Tarbitz 23:3/4), there's a little evidence:
"The Islamic tradition tells us that the two largest Jewish "tribes" of the city [Almedina], Nadir and Qurayza, were kohanim. This is mentioned in dozens of stories and also in songs from the time of Muhammad. Dr. C. Z. Hirschberg, in his book "Israel in Arabia", pg. 167 and 309, doubted the historical credibility of this fact, for we have found that the Jews of Almedina didn't always follow the laws of family purity required of kohanim. But is Almedina any better than the district of Meishan in the land of Babylon, the center of Judaism, about which Chazal tell us:
"Rather, the priests who were there were not particular with regard to the prohibition against priests marrying divorced women." (Kiddushin 72b)
And from where do we have evidence that this Jew of the Jews of Almedina, that didn't strictly follow, was a kohen like the rest of his brethren? The drash that is attributed to Rabbi Yochanan on the verse: "In the steppe in Arab you will lodge" on the issue of the pirchei kehunah who escaped to the Ishmaelites, likely reflects not just the cruelty of the Nabateans during the time of the Second Temple, but also events that were closer to the time of the midrash. It seems to me that the Jews of Almedina, who were farmers, owners of date plantations, came there at a quite late era, perhaps due to to troubles from the Byzantine rulership; for the Jews of Arabia mentioned in the Yerushalmi (Ketubot 59a) were merchants, for their possessions included camels and perfume, while the Jews of Almedina were people of settlements of such form that they had to hire camels when they went into exile. It seems, therefore, that they came to Almedina as one group, perhaps from Yericho or another area in Emek Hayarden which grows dates (later, there are records that some of the refugees of Almedina came to Yericho). And now, the centralized settlement of kohanim, cities of kohanim, were known both in Israel and outside of it...the reason for this being most likely because it was easier to keep the laws of purity that were special to the kohanim in those times. There's some basis for this, that kohanim moved to the land of Arabia in entire groups..."
I'll add that it seems that S.D. Gottein was slightly mistaken, because while the Banu Nadir were plantation owners, the Banu Qurayza were merchants.
So it seems that Arabian Jews were known in Israel around the time, and in particular, those who may have eventually (or perhaps even then) became known as the Banu Qurayza, who were merchants.
In Mendel Wohlman's Mistarei Ha'aggadah, he writes on the story of Rabbah Bar Bar Chanah and the "metei midbar" (dead of the desert)(Bava Batra 73b):
"It is very hard to imagine that these dead people, that RBB"C saw were those who left Egypt and died in the desert, for after Rabbi Akiva ruled that they had no part in the World To Come (Sanhedrin 106), then they were evil people, and why would they earn the right to have their bodies preserves for thousands of years? However, we have heard that in the Arabian Desert there are Jews from the descendants of Rechav; these Rechavites, like all of the Jews of Yemen, wear all day long a tzitzit over their clothes and sleep with it also at night, and they are strong, armed warriors riding on camels and raiding caravans and extolling from them a tax (see the book Even Sapir). These Rechavites are the dead..."
So that's another view, that Chazal were aware of caravan-raiding Arabian Jews. While the Banu tribes of Almedina were not known for being raiders, it's not such a far-fetched thought that this may have been what some of the Arabian Jews did at certain times, especially when considering:
a. There were Jewish pirates and also Jewish Listim over history (and forget about the Jewish mafia and gangs of late 19th and 20th centuries).
b. Caravan-raiding was (and is) quite common in Arabia (Muhammad was a caravan robber).
c. As the kohanim of Almedina didn't rigidly follow the laws of family purity, it's possible that there were Jews who also didn't see any real problem with raiding caravans. It's also possible that these were sort of the "enforcers" of the rest of the Arabian Jews, who wandered the desert and attacked any passersby who may have posed a threat to the other Jews.