The invitations often offer discounts on designer labels, but they are from spammers, not the brands they claim to represent.
Whether the recipient accepts or rejects the invitation, it notifies the spammer that the message has been received, so that more can follow.
Sometimes they take the form of photo-sharing alerts.
Rather like spam email, the invitations are sent at random to huge email lists, and they appear as calendar notifications.
The flaw has existed for a while but has only recently been exploited, particularly in the run up to Black Friday.