There's not a great deal you can do about the situation for two reasons. First, you have no ability to change your cancellation policy with daycare. It is same day, and the client will receive a full refund if they cancel before the service has started. Given all the communication between the two of you, the client, if they decide to just cancel at this point, will receive a full refund.
Second, and more importantly, your profile states that you or your boyfriend are home all the time, as you work from home. Therefore, they could easily make the case to Rover that you were not in any way inconvenienced.
My suggestion is to just let it play out. I can't imagine why anyone would still need daycare that late in the day, at least 5 hours later than the original drop-off time. In addition, you need to outline in your profile the hours during which daycare is offered. State the hours for dropoff and the hours for pickup. If this pet owner decided to drop off the drop in the late afternoon, when were they planning on picking it up? Most sitters say that daycare ends at 6pm or thereabouts. You will need to make that determination and ensure that pet owners understand your hours of operation.