Yes it's small but it's hard wood and it' needs to be removed so as not to damage the wall or cause more cracks
It's probably still growing inside the roof
The crack will be letting in water that will eventually lead to significant damage, it will also grow as water in it freezes and thaws over the winter months. Ultimately though if the owner doesn't seem to be too bothered, you need to let it go unless it is directly affecting your property.