Zense wa Reikoku Koutei, Konse wa Youjo - Ch. 6 - Clenched fist

[N2O]

I need some minor explanation since English isn't my first language, if I look gutter cleaning I see a bunch of guys cleaning that part of the ceiling, but if I see the image of her workplace, she's holding some cloth and there's a bunch of rocks in boxes in the back so is that really what she's doing?

As KagamiGaSuki said, a gutter is the thing at the side of the road that redirects water into the sewer system. Cleaning these for a job is typically associated with someone who is very down on their luck and just needs any work to stay afloat. So it gets looked down on a lot, and is sometimes used as an insult