Based the information in this post, at least 2 user requests, and the known unpopularity of any tool which scrapes fedi timelines to make posts more publicly searchable without consent, I have fediblocked zeitgeist.blue from #TootCat. 
(All TC admin decisions are subject to revision if there seems to be a consensus towards that among TC users, either at the time or later; feel free to weigh in with your position, either for or against. ^.^)
@woozle personally since this app seems to potentially feed private or non-public messages (e.g. followers-only) to Anthropic, I think it's fair to block it. If it only does it with publicly visible posts, and respects nobot/noindex tags on people's profiles, then I would be/am ok with it. (It's not 100% clear on which one it is, but a cursory glance suggests it feeds your entire timeline to the chat box).
(Some) people on here are extremely sensitive to anything perceived as "scraping", and will pile a lot of hate on indy developers (see also Searchtodon https://searchtodon.social/Adventures-in-Mastoland.html), which I find naive and misplaced. Anything that isn't locked down will have been hoovered up a hundred times over by every AI or SEO or whatever startup from California to Shenzhen, not to mention duplicated/federated to much of the fediverse network, including many instances with very dubious proprietors. But someone stores a copy of their feed to their home server and suddenly they're the devil himself. Have some sense of perspective.
That said, this app does seem to pose some real risks of feeding non-public data to a very questionable entity, so I support blocking it.
All good points, and in alignment with my thinking as well.
FWIW, fortunately, the admin panel showed zero connections between TC and that instance at the time that I blocked it. (We managed to close the barn-door before any of the horse had escaped. ^.^)
Woozle Hypertwin
Arne Brasseur