Yale left an incarnation in the inn taking care of his disciple and left the world following the contents of the envelope left by the Battle God.
Given the information obtained there, they would need to face a long trip and departed immediately without telling anyone else about it.
The incarnation left by Yale was weaker than his real body but was still enough to be the most powerful existence in the world, so it didn't matter too much as it would still serve to protect his disciple's body while he was in the life and Death Trials.
As for the room in the inn, no one dared to ask for it, and soon the owner announced that the inn was closed and, in its place, a church would be constructed.
The owner was quite sharp at business and didn't doubt on using Yale's fame to make money by turning the inn into the main place to pray to Yale.
Yale's incarnation noticed it, but he didn't mind as long no one disturbed him.