In the episode 20 of the first season of Bakuman, there's a promotioner lady giving out something (somewhat iPhone shaped), but the surroundings are static and it doesn't look like anyone is taking whatever she has.
Considering the anime is about manga production, I suppose the square where this lady is standing might be close to the Yuueisha building, or even the promotion is directly affiliated with the company, but I have no idea what this item could be.
Although I agree with you based on the size of the item in her palm that it looks like the size of a smartphone, it makes most sense to assume this is supposed to be a packet of white tissues (which should be drawn slightly smaller than it is in the close-up shots) because 1) tissues are the most common of such items to be handed out in public places throughout Japan, 2) many Japanese blatantly ignore and walk past the people giving out tissues without taking them, 3) they are often carried in a small plastic basket (though her basket visually looks like it might be wicker or some other material I've never seen one of these workers use in real life), and 4) they are given out year-round. I have on a couple of occasions seen clear files or lotion samples given out, and of course flyers without a take-home goodie, but I have never seen something on offer that looked like a white cell phone slightly larger than a packet of tissue.
