Hunting Trophy does not apply a buff icon to characters, like other buffs.
When zoomed in, placing and removing the Hunting Trophy has no noticeable effect on movement speed.
This has been observed in two different rooms, but especially the school entrance. Since characters can't be "active" in the school entrance, which is a requirement for many of the the wall items, Hunting Trophy is one of the few items that makes sense to place there.
Related, but I recommend adding an action to the school entrance for a character. Perhaps make it like Gazebo, with characters adding a tiny amount of prestige to school (.001) and stopping there for a brief moment. This way more items "work" when placed there.