It didn't surprise me to see they teamed up with the detective, but the way he was introduced felt forced and rushed. That aside, I think them going on official alien killing missions is a great way for the story to go forward.
Sorry, I wrote my opinion in Spanish.
I'm really bad at English, but I’ll try.
I thought Iglaskar was going to hunt down the protagonists, but aside from that, we’ve learned more about the manga’s world. There are more people who hate the aliens besides the protagonists.
One thing I liked was how the protagonists "took care" of each other Nomamoto throwing curry all over Iglaskar's face, while Kitami tried to prevent them both from being imprisoned.
I liked that interaction because it shows (even though it’s mostly because Nomamoto needs Kitami to kill aliens so he can eat them) that they care for each other a little or at least that's what I think.
I also liked how they don’t trust Iglaskar. It’s better to keep their secret. Still, what could happen if others find out about the true forms of the two protagonists? It’s an efficient solution, especially considering everything they do to get rid of alien corpses.
Another question that came to mind is how dangerous the luxurious alien hotels are. What dangers could be there? Maybe I’m overthinking, and it’s just armed aliens, but we barely know their technology. How powerful could it be? Are there even stronger aliens?
It’s fascinating, and I want to know more. I HAVE TO WAIT ANOTHER WEEK, HOW FRUSTRATING AAAAAAAAAAAA
Anyway, I like how the story is progressing, and I hope I can keep writing my Drama Queen reviews.
Sorry if there are any errors in my review.

I personally can't see what would have happened in between if it the detective thing happened over a longer period of time so I don't mind it being done this way personally. I would have liked to know what he thought about the body eating though but I guess we'll find that out at a later date (probably for the best in terms of negotiating power though)