Corrected entry: Why must Chakotay use a pen and paper to record his memories of Kellin? There is no justifiable reason that his recorded voice should not be able to be preserved just because he's talking about Kellin.
Corrected entry: If Kellin spent multiple weeks on the ship, certainly there would be security surveillance evidence that she was there. Even if she didn't visually show up on the video, people would be seen interacting with an invisible someone. Similarly, the Doctor would either be able to see her and remember or not be able to see her and figure out that people were interacting with an invisible person. And what about the ship's logs? People would certainly have talked about her in their logs.
Correction: It is mentioned in episode that not only can the memories about her race not be retained by the few other species that they meet, it is also stated that they upload viruses into the computers of any species they meet in order to erase all knowledge of them from all databases (including sensor logs, sensor scans, crew logs and presumably the EMHs memory circuits). This is why Chakotay writes his final log entry for this incident by hand so that it can't be erased.
Correction: This is explained in the same episode - when she left with the fugitives they planted a virus in the computer that wiped out all traces and records. Presumably this same method would be employed by the security force that was to retrieve her.