The Internet Archive does not respect robots.txt - https://blog.archive.org/2017/04/17/robots-txt-meant-for-sea...
> Some sites are not available because of robots.txt or other exclusions. What does that mean? Such sites may have been excluded from the Wayback Machine due to a robots.txt file on the site or at a site owner’s direct request.
If you exclude them in your robots.txt file they will also absolutely retroactively remove your site from the index.