That black colored rhombus gem was the Stone of Fear.
The stone was created by Little Cart's powers as a Tsukumogami with the ability to store the emotion of 'fear'.
If bizarre deaths were happening in a certain area, those from the Department of Mysteries or the Deity Rising Palace would definitely send someone to perform an investigation. Considering Mitsue Natsume's status back then, he would have definitely received the news beforehand, which allowed him to keep the Stone of Fear immediately. Then he would wipe out the demon instantly without further hesitation.
When Kimura Kazuki arrived to investigate the matter, Mitsue Natsume could perceive his abilities. He thought of giving up on the demon Natsuna Yamanaka. Still, due to the use of the Six Emotions Spirit Regeneration Spell, his control over Natsuna Yamanaka turned weak, which had caused some delay. In the end, Natsuna Yamanaka was exposed and got caught within a day!