Over the last few weeks many people have been reporting unwanted Calendar invites, usually looking like junk email with a sales pitch and links. It is difficult to get rid of these invites without notifying the sender that you either declined or accepted it. But there is a method to quietly delete the invite. A better solution is to switch to email notifications of Calendar invites until Apple fixes the problem.
Update: You now have a “Report as Junk” button on Calendar invites if you look at the Calendar in iCloud.com. So if you get one of these, the best way to handle it now is to log on to iCloud.com in the browser, view the invite in the Calendar app there, and hit that link. It deletes it without notification and also tells Apple about it so they can track and perhaps block that IP address or block. I expect this same button/link to appear in the Calendar app in iOS and Mac at some point in the future.
Another approach is to create a new calendar called Junk. Move the invite to the Junk calendar, then delete the Junk calander. Rinse and Repeat until Apple fixes the problem.
I used a combination of Gary's and Mike's solutions: Mike's 'Junk' calendar solution worked perfectly as a one-off for the ones that had already come through (which can't otherwise be deleted). I then deleted the Junk calendar, and set up Gary's approach (in the video) to stop any new spam invitations — it's been successful! Thanks for sharing your tips — those spam invitations were a real nuisance :-)
Mike: I show exactly that in the video. Maybe you didn't watch the whole thing?