There's 2 options, either Itsuki did it all by herself or yotsuba was helping out. If it was the former, then it would make sense to not give the photo to yotsuba. That would neatly explain why she brought the charm to the hospital, since she knew from chapter 1 when she look at his handbook.
That said, I'm still leaning on the latter, yotsuba asked itsuki to help her make Fuuts move from their past. Reason is of the sheer timing of Yotsuba jogging by, would explain who was the person overhearing their conversations in the dark, also about that bubble where itsuki said yotsuba passed her clothes to her.
Also if it was itsuki all along, that apology at the end of the last chapter would be "yeah, sorry" tier of apology.