@Justin1032 Most people would take the fact that the cleaner has arrived and begun cleaning as something much stronger than a "nudge." But it does happen from time to time that the guest (or even the host) is mistaken about the scheduled checkout date.
If the current date is still available, you can ask the guest if they need to extend their booking by an additional day. If not, it should be sufficient to inform them that you need them to move along so that you have sufficient time to prepare for the next arrival.
In the future, you might consider sending a default message to all your guests the night before, to thank them for their stay and remind them of the next day's checkout time, along with any instructions for departure (such as how to lock up and return the keys).