(There should be a Move link at the upper right of a post, so you don't need to open another thread. )
You can't stop the form from accepting submissions from other addresses unless you drop the Email Address field from the visible form. The big problem with this is if a person who wasn't in the original recip list clicks the link to your LP, not only will their click be registered to the original recipient (which always happens) but they will have no chance to supply their own email address, so the form submission will also be registered to the original recipient. This is likely much worse than what you're experiencing now, since you'll have RSVPs from humans that look like other humans.
You can of course filter the submissions by the original Smart List and sort people into shouldn't-have-done-this-let's-reach-out and original-recipient-ok-to-attend.
I also want to channel Josh and wonder what's so bad about people who want to RSVP who've been referred by your qualified leads (at least vs. blocking them entirely).
If this is a closed event, such as Customer Advisory Board, where you only wanted specific people, you can do the following:
Add a program Status of "Wait Listed" and then manually check that membership list to upgrade them to Registered to send the Confirmation.
While you can add an exclusion on the Registration Trigger, like "Fills Out Form+Member of RSVP List" then the other person will get nothing and have a bad experience.
But yes, that's the only situation where I might deliberately wait list or exclude people.