If someone requested access to your appointment before you closed your appointment and you did not approve or deny the request, that request remains pending in the Requests for Access tab of the appointment and you will continue receiving emails about it. This is because, without a response, the requester may not know the status of the appointment or if you still need their support. You can handle this request exactly the same way on a closed appointment as you would on an open appointment.
To clear the request and stop receiving email notifications about it: Navigate to your closed appointment either by clicking the link directly to it in the email notification or by navigating to My Appointments and checking the checkbox to see only your Closed appointments and locate the one in question. For a shortcut, look for a red "Pending request for access" icon by any appointment (closed or open) that has a pending request:
Click directly on the red icon or navigate to the appointment's Requests for Access tab, then click on the blue name of the requester. Enter a Decision. For closed appointments, you usually Deny the request noting that the appointment has since closed; however, approving it would still give the requester access if, say, they need to review its information but not enter activities. More on processing the request
After successfully processing the pending request, you will stop receiving emails about it. In the future, a streamlining step while closing an appointment is to note any red text warning on the appointment itself (such as "Pending request for access") and handle it if needed before closing the appointment.