Many organizations today have identity cards, and use passwords and multi-factor authentication to authenticate and authorize people. If there's trouble, things can be done: Identity cards can be replaced with new serial numbers; passwords can be changed; digital certificates revoked; keys and locks changed.
If your organization can travel in time, most of these methods break down. If my password is compromised and a malicious actor can travel in time, then revoking it from 'now' doesn't help, and ensuring that password is never issued just means that password2 is compromised instead. You also can't ask someone to look over the access logs and verify it was all them, because it might be them, it just might not have happened to them yet.
On top of that, changing anything when one of your own is out of sync with you, means that they could return and give the incorrect passphrase, or have the wrong key, or simply return at a point you're not expecting them to.
How would you reliably identify a person who's a part of your organization, assuming there are too many people to simply memorize?
The best I've come up with so far is that each person on each journey gets a unique code. Whenever they return, they can be connected to a specific trip. It does mean that all the codes would have to be determined in advance, though, and still suffers from problems if the list of codes is compromised.