I have a new issue:

I have an K2 item: category/sub-category/sub-sub-category/item

I'd like to have item image only on sub-sub-category site, therefore I activated on Item page image to show in "Item view in category listing". It works for sub-sub-category, but I have the unwanted image on sub-category site as well. Category site is ok - no image from item.
Category - no image from K2 item
- sub-category - image appears -> this is to remove
- - sub-sub-category - image appears -> it's ok.

How could I remove item image only from sub-category site?

You need to edit each category's settings separately.
Keep in mind that if a category is inheriting its settings from another category, you need to edit the 'master' category's settings.

I don't have inherited parameters from other category.
In this case, what would you recommend to do?
Which parameter of this category responsible for this issue (unwanted item images on category view)?

The setting you need to edit is:
"Image size for primary items" and select None.
We are talking about K2 images, right? Not images uploaded through the editor.

In this category under "Layout grid" the setting is "Image size for primary items -- No image --"
(I uploaded the item images under item/basic/image . . . (where i can edit Content | Image | Image gallery | Media | Extra Fields | Attachments)
It means, images aren't in the "content field" uploaded.

At your category "Display Settings" -> "Item view options in category listings" -> "Image" set this option to hide.

At my category "Display Settings" -> "Item view options in category listings" -> "Image" was already set to hide...
In the meantime, following your direction, I changed category setting under "Layout grid", but now at "Image size for leading items -- No image" as well, and -- miracles will happen -- images got disappeared!
Many thanks for your help again! :)

You 're welcome :)