This is a possibility that there aren't any great solutions for currently. Can you message me on reddit with the link to check?
In the absence of a reporting mechanism for issues like this, I'd suggest at least a notice / message alongside results to indicate that they may not reflect the current state of official and amended records.
(I think you may be wise to take this issue fairly seriously; there's a risk of people considering the search engine to be an authority in itself -- which, to be fair, is already a risk for any search engine, but since this one is more domain-focused, it's possible that some users could overdevelop a sense that the results are accurate and complete)
Everything else should not be searchable.
1) People don’t read terms. Should they? Yes. Do they? No.
2) This language is more like a disclaimer than a term of use. I would not assume that disclaimers about the accuracy of the result would be found in the terms.
So yes, the terms link is prominent, but no, I don’t think it addresses this issue.