Sometimes people have accidentally posted identifying info or objects. In those cases staff has removed them.
This seems like a different issue, where the obsever is knowingly (I assume) posting personal information to a public site, although they may not be aware of the various risks involved. IMO it’s best to inform them that their personal information is now freely available online and reach out to the instructor if possible, or encourage the student to do so. You’d hope the instructor will at some point see comments on their students’ observations…
For what it’s worth, nearly every new account gets a welcome email and that email includes a link to the Teacher’s Guide:
And the Teacher’s Guide recommends not doing this:
We recommend that you not have your students include an identification card in their photos in order to prove they’re not plagiarized. iNaturalist observations are viewable by anyone on the internet, and identification cards and passports contain sensitive information which can be exploited for nefarious purposes. If you don’t feel you can trust your students to submit their own images, then iNaturalist may not be a good fit for them.
Also, see related conversation: https://forum.inaturalist.org/t/is-there-some-sort-of-resource-that-suggests-students-be-asked-to-include-an-id-or-token-in-their-photos/27334