@Shugarry
After re-reading I think that was her excuse to Moko-chan, because she was caught with her head over the moon thinking about Ren to the point that she hitting the wall.
So much so that she has already talked to the department chief about going on school uniform.
As I see it. It was a shackle, as Ren said it, so Ren could keep Kuon under control. When he was playing that serial killer, he was afraid Kuon would surface, as it did. The Heel Siblings Arc.
When Kyoko become the love charm that make Ren forgive Kuon, the watch lost it's usefulness...