I don't mind as long as the child is sharing...as soon as he/she gets possessive or it causes the slightest argument it goes away.
When kids bring small things, I tell them straight away that this needs to stay in your backpack so it doesn't get lost....and this is exactly what I would have done with this box...stuff like that wouldn't have made it past the foyer! However, a barbie, or book doesn't bother me.

When Mom comes to pick her up tell her that it needs to stay home as it caused mess and arguments and isn't really appropriate for this setting. Good luck!