Late arrivals are a planning input, not an irritation
Whoever reaches a list that has closed is telling you something worth keeping. Marta runs quarterly sessions for a design community and started counting the too-late messages instead of apologising through them; two quarters of that count told her whether the cap was wrong or the start time was. The people arriving after your cut-off are the same evidence.
For a session that runs again, the graceful ending is a next step: the closed page, your reply, or your announcement all pointing at the next date's own page โ because one webinar page holds one session, and a second date needs a second page built for it. For a one-off, honesty is the whole offering: it happened, the replay and slides went to the registered list, and your queue for the next one is open.