Implement the scheduling inbox mechanisms as specified in RFC 6638. The process is described in 4. Processing Incoming Scheduling Messages and therefore is not repeated here.
This goes in conjunction with Wallace which automatically processes incoming iTip messages and already creates or updates the according user calendars. The original iTip messages shall be stored in a dedicated place/folder once processed by Wallace, where iRony can pick them up and present them to the requesting CalDAV client as "notification". Once the client has fetched the notification from the scheduling inbox, it deletes it.
We should therefore first define a dedicated storage for this CalDAV scheduling inbox and not (ab)use the email inbox for this. As an alternative, Wallace could set a custom property to calendar event after applying an update from iTip in order to flag it as an "inbox item" for CalDAV clients. When iRony then receives a DELETE request for that inbox item, it'll simply remove that property from the calendar event.