If I’m understanding this correctly, you were offered a sit without a listing/listed dates? As in, they messaged you and asked “Do you want to do this sit?” without sending a confirmation request? If so, then no, that sit is not confirmed in the THS system and you will have no protections (or ability to leave a review). If you want to do the sit, ask them to send you a confirmation request. Once you get that, you hit confirmed and it becomes one of “your sits”. There is a paper trail and an ability to leave a review.
Hope that helps.