[after midnight]
Her name is Hanyuu. She was sacrificed, a long time ago, for the sake of her village, and became the village's shrine god.
[The shih-tzu starts snuffling at her hand, having been ignored all this time, and she idly starts to scratch between its ears.]
Then she became really close with one of the shrine maidens, Rika, who was murdered. So she took Rika back in time to stop the murder, but it kept happening, and she kept having to take her back. They've been living the same few weeks for thousands of years now, trying to find a way to stop Rika's murder.
[Glancing back up at them.] It sounds like it'd drive you crazy, doesn't it?