Vol. 35 (Ghost Case) and Vol. 70 (Burning Dog Case) could help understand the trick
We're not far from Mount Takao, the Tengu Mountain (vol. 11), and it happens the old priest looks like Mr. Hawk, who looks like a tengu. Funny because tengus are either crow-like or eagle-like. Karasuma is a crow tengu, and Mr. Hawk/Ooka/Momiji's grampa (according to me) is a hawk tengu. Let's hope nothing bad will happen to the crew