Invited marks are recorded. The Matrix chapter details how an invitation includes a duration, and if you log off and return to the Matrix before the duration expires, you are automatically extended a new invitation to mark that host until the duration is up. Presumably, a spider or HR manager can view and edit the list of invited marks, to remove invitations from people who have resigned or been terminated so that they can't continue to access their former employer's host. The Patrol IC program is specifically shown in one of the hacking examples to go around examining personas inside the host to make sure they're supposed to be there, and it mentions the decker in that scenario hoping the spider isn't around to make his own Matrix Perception checks.
A successful Matrix Perception test can identify a unique persona. Should a Patrol IC or a valid user (maybe someone that says "Hey, I don't recognize that icon..." or a watchful spider on patrol) identify a persona that doesn't belong on that host, it's safe to assume they'll set off an alarm. In a corporate environment, the ordinary users probably just notify the spider, giving you a bit more time before the heat really comes down (the spider needs to verify the problem before deploying the IC that can shut down production). In a more public environment - like a club - ordinary users probably have no clue who is and isn't allowed in, and thus only the spider (if there is one) and Patrol IC (if they're there) are likely to spot you.
Running silent is a double-edged sword. It allows you to actively resist being scanned by Matrix Perception tests, but if you're found running silent on most hosts, they'll automatically assume you're not there legally. Hard choices all around.
On a final note, this is one of the few places where a Technomancer truly shines over a decker. Using the Puppeteer Complex Form, the Technomancer can cause a device to use the Invite Mark action (marks: 3; duration: unlimited). Assuming invited marks from slaved devices also give marks on their masters (the way hacked marks do), you can get onto a host's list of invites that way. (That part is really subject to GM interpretation, though, I'm afraid.)