I'm not sure that you can. I think the whole point is that you send out an invitation, which should arrive in your correspondents' mail clients in a form that will prompt them to add it to their own calendar, and in doing so will, hopefully, prompt each user to set a reminder to suit his own needs.

Ideally you would upwardly delegate this kind of reminder to the calendar host so it would do this reminding task automatically on your behalf, rather than relying on you doing something by hand. After all, you may well forget too. ;-) But the calendars I have worked with have not as far as I can see offered such a facility.

Maybe my question should have been, How can I change the reminder pop-up into an email or text message?

What I am actually trying to do is to send a reminder message to my cell phone at some interval prior to my appointment. I have my phone set up as a "person" in my contact list. It can be the recipient of the reminder.