Pg. 52
We have run into this causative form + もらう a time or two before in this manga. The earliest example all the way back in chapter 1. Here is my post, with a link talking about させてもらう included, from that discussion thread:
それでも歩は寄せてくる | Week 1 Discussion ♟ - #37 by MrGeneric
Editing to add the link I referenced since the post doesn’t show up as a dropdown like it usually would: https://forum.wordreference.com/threads/させてもらう.3790593/
The gist of it is that させて+もらう, while a permission-requesting statement, can also carry heavy vibes of, “This will happen.”
Basically saying, “Hey, is it okay if I do this?” while already doing it, so to speak.
In this case:
取る becomes とらせて and もらう is added on.
とる means “to take,” but can have a meaning of “to win.”
In this instance, I would read the sentence as:
“Sorry, but we of group 2 will take (with the take meaning “win”) this relay!”
悪いが = Sorry, but
このリレー = this relay
2組のオレたちが = we of group 2 with topic particle
とらせてもらう = “will take,” is the cleanest English translation, but would really be “will have you let us take,” which is unwieldy and awkward, but preserves the “permission” aspect of it.
Though again, it isn’t actually asking permission. It’s a reflexive politeness thing masking a “this is happening” feeling. It’s really weird, for sure, but the mangaka really enjoys this construct, it would seem.