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If Site A links to Site B, the link exists on Site A.

If Site B blocks the SEO bot, the seo bot can still crawl Site A which is where the link is located. Thus it can still see the link.

The...

The OP is talking about hiding their link profile from competitors... So regardless of whether or not your site blocks the SEO bots, they [the bots] will still see those links on the sites that the...

That would only block them on your site though - not the sites that contain the links to your sites, which they'd still pick up.