I heard an awesome answer in a Dvar Torah given at our shul awhile ago:
The idea starts from the selling of Yosef into slavery: The Yishmaelim who took part in the deal were said to be
"...a caravan of Ishmaelites coming from Gilead, their camels bearing gum, balm, and ladanum to be taken to Egypt." (Genesis 37:25)
Gilad is significant to the story as it was apparently a center for slave-trafficking (unfortunately I don't remember if a source was brought for this part and I couldn't find anything...).
Later on in the Torah, it is said that Yosef lived to see his grandchildren through Machir, son of Menashe:
"...the children of Machir son of Manasseh were likewise born upon Joseph’s knees." (Genesis 50:23)
Who were these descendants of Yosef that were "born upon [his] knees"? One was Machir, who was apparently named after the Mechirah, the sale of Yosef. Another was Gilad, son of Machir and father of Chefer, who was apparently named after the city of Gilad. These two, among the other descendants of Yosef, grew up hearing his story of the sale, his life's story. If Gilad wasn't a center for slave-trade, perhaps he wouldn't have been sold into slavery and wouldn't have had to endure all of those hardships. At his deathbed, Yosef told them not to forget what evil came from the Gilad and to make sure to rectify it. Machir and Gilad received their names so that the Tribe would never forget.
That's why Menashe's descendants go out and capture the Gilad without prompt or permission from anyone - it was always a given that this was a personal mission for the Tribe of Menashe that had to be accomplished:
"The descendants of Machir son of Manasseh went to Gilead and captured it, dispossessing the Amorites who were there." (Numbers 32:39)
and that's why Moshe readily gave them the land:
"So Moses gave Gilead to Machir son of Manasseh, and he settled there." (Numbers 32:40)
Having fulfilled Yosef's dying wish and clearing out the evils of the Gilad, they proceeded to settle there.
Another answer is brought by Da'at Mikra in their introduction to Divrei Hayamim, pg. 65-66 (my translation):
"And explained the author of the ancient commentary to Divrei Hayamim, known as "Student of Rasag"...that this whole portion in Bamidbar, end of ch. 32 (and afterwards also in Devarim 3, 13-15), in the lands of the families called "the sons of Menashe", who set out and conquer large territories in the north of the Gilad and the Bashan and naming them after themselves...are "ancient tales" (i.e., stories from the past). As he says:
"And Machir, his mother's father, was the head and chief of Gilad, and Yair conquered the Gilad after him, therefore he was named after his mother's father and after the name of the territory that they conquered during the reign of Yosef whow as king over all of the land. And when Yosef and his brothers died, the nations grew stronger and Geshur and Aram who were nations took Chavot Yair etc - and for this the sons of Machir desired to dwell in the land of Gilad, and per the conquests of their forefather, Moshe gave it to them...and know that those things...of Machir and Yair and Novach are ancient tales, because Machir and Yair and Novach did not capture anything [during their time] in the desert..."
And that is also the view of Rabbi Yehudah Hachassid (in his commentary on the Torah, Shemot 1:7)...:
"My father would prove from Divrei Hayamim, that in the duration of Yisrael's settlement in Egypt, they would sometimes go to the land of Yisrael, the ground [owned by] our forefather Yaakov, and would build there cities. And I believe, that specifically the descendants of Yosef would do this, and they had permission from Pharaoh, because out of the respect he had for Yosef, Pharaoh honored them by letting them repair and strengthen their inheritance, and they would settle there tenants and would collect from them taxes...therefore, that She'erah who lived well for six months prior to [Yehoshua]...must be that it was during the time they were in Egypt."