Yes, ideally you add them on before you confirm the booking. Use the "modify" function to add in what is necessary. Since you have a daycare fee, you could use that or just put in a flat amount under modify for the additional time. It really helps to find out when the pet will be dropped off and picked up before finalizing the booking so these adjustments can be made and the owner understands that each night of boarding is only good for up to 24 hours of care,
I do allow a bit of leeway and won't charge for an extra couple of hours, but I don't tell them that. Instead, when we discuss times, I will tell them their pet needs to be picked up by the same time as they dropped it off with me. They do understand that.
If you haven't billed them in advance, you can always initiate a separate booking yourself. However, they would have to agree to pay it. I find it easier to get it done before an engagement starts.
I just had one of those myself over Memorial Day weekend.. Since I don't offer daycare, I added in my fee for taking care of the pet until the agreed-upon time, using the modify ability. In this case, it was a late evening pickup, so the owner got charged for another full day.