Gotta love how Aoba always materializes when a possible scandal comes up...
This is a pillow.It's a trade practice where one trades sexual favors in exchange for jobs.
Analogous to English "casting couch".
Ohh... you meant that pillow!! Naka-chan jumped to the wrong conclusion there a bit.☆ Tee-hee!♡What do you mean...?Eh, it's no biggie. You can sleep even without a pillow.That's no good, Kako. If you don't pick a proper suitable one... your pillow won't match you and you might end up sleepy all the time, you know?
WHOOSH
...What's this about 'that' pillow...?
Wait wha—!? You really went and did it!?
I-I don't think you should do that...!
Naka-chan doesn't do any pillow stuff!!
This is the pillow business.No, no! I said I didn't!! Well, I did proposition someone before, yes, but he rejected me, saying, "This is not what I want from you...", so it doesn't count, okay!! It's a sack-shaped cloth stuffed with cotton, buckwheat husks, feathers, low-resilience polyurethane, et cetera.
You use it as head-support bedding when you sleep, by putting your head on it.