The beginning of the narrative involving Miriam and leprosy is Bemidbar 12:1:
|א וַתְּדַבֵּר מִרְיָם וְאַהֲרֹן בְּמֹשֶׁה, עַל-אֹדוֹת הָאִשָּׁה הַכֻּשִׁית אֲשֶׁר לָקָח: כִּי-אִשָּׁה כֻשִׁית, לָקָח.||1 And Miriam and Aaron spoke against Moses because of the Cushite woman whom he had married; for he had married a Cushite woman.|
Rashi actually asks the question -- or rather cites the Q and A from Tanchuma Tzav:
for he had married a Cushite woman What does this [apparently superfluous clause] mean to say? You find a woman who is beautiful in appearance, but unpleasant in deed; [or a woman who is pleasant] in deed, but not of beautiful appearance. This one, however, was pleasant in every respect. [Therefore, she was called Cushite, as above.] - [Tanchuma Tzav 13]Yet there is in fact a rather simple, peshat based account for the repetition of כִּי-אִשָּׁה
כֻשִׁית לָקָח. Let us look to sefer Yonah.
sefer up to this point did we have Yonah explicitly tell them that he had fled from the presence of Hashem, yet the men knew. Why? The pasuk fills us in to the otherwise unknown, and until now, not relevant, information.
Similarly here in parshat Behaalotecha. All of a sudden we here complaints about Moshe's Kushite wife that he had married. But what is this of a Kushite wife. So the pasuk clarifies that he indeed took a wife from the Kushite nation.
That is, on a peshat level, we do not assume a closed-canon approach, and when we some previously unknown character or event is mentioned, sometimes it is deemed necessary to state -- "Oh yeah, Moshe had married this Kushite woman, so this heretofore unknown event was the cause for Miriam's complaint."
Why does Rashi -- or rather, Tanchuma, not give this answer? Recall that this operates on the level of derash, and so the principle of omnisignificance applies. Therefore, the repetition has weighty meaning in its own right. Futhermore, midrash often operates on the the principle of the closed-canon, and therefore this is not some new, heretofore unknown Kushite woman, but rather is Tzipporah. (As is evident from the answer, and the surrounding Rashis/midrashim.) Thus, the Torah is not explaining some otherwise unknown person. (Perhaps it would still be explaining a heretofore unknown event - reading lakach as divorce, we are told here thgat he divorced Tzipporah - which is where the first part of the answer comes in.) Therefore, the repetition of this fact has some midrashic significance.