That ring is only meant to leave Iris hand when its being given to her betrothed.
Trying to give the ring back could get him killed to protect the secret of how it was stolen.
KonoSuba 3 – 06 – The Man in the Mask
When Kazuma and Iris switch bodies again, it leads to Kazuma being banished from the palace, which is when Chris meets up to discuss Divine Treasures. Kazuma tells her about the body-swapping necklace, and learns that it can be extremely dangerous in the wrong hands, as one can kill the person you've swapped bodies with and…
