What the Bough will find itself connecting to is the memories of Tsurumaru! While the current state of him definitely is in no distress, and in fact, seems somewhat comfortable and self-assured, the Bough will be able to pick up a memory of emotion. There isn't much, and there are no details, but there is the sense of grief and confusion. Dante can't pick out a time that this happened, what happened to cause it, or any other details, but the bough manages to pick up this much before the connection seems to be shut down very aggressively. Whether they've been forced out, or recoiled from something, it's hard to say, but the burst of emotion was particularly strong.