Wayback Machine is aware that this could be a problem, which is why they let website owners expunge sites.

And what a surprise! So does Bing: https://www.bing.com/webmasters/help/bing-content-removal-to... (As do Google etc.)

Neither of these expunging mechanisms work if you're not the domain owner, however, so this is just one more reminder that any content you upload to somebody else's website is never fully under your control.