1. Just to make sure - please check that you are using the latest version of DayPilot.Modal from here (2.7):
2. The Modal.Close() method defined in Daypilot.Modal-2.7.cs/Daypilot.Modal-2.7.vb can be called on the server side from the modal content page to close the dialog. It's not possible to close the modal on the server side from the parent page.
If you have the modal instance reference ("modal") you can call .close() method:
If you don't have the instance reference (e.g. in the modal content page):
If you call DayPilot.Modal.close() from the modal content you need to include modal.js in the content page as well.
Let me know if it didn't help.