Yes - you will have to stop respective crawlers reaching your site such as bots for moz, majestic etc - which in turn means that these data providers are unable to collate and provide data on your website... You need to amend your robots.txt in order to do that... making sure you do not block out the search engine ones like G, Bing etc

In addition just to confuse your competition even more you can hide some of your most authoritative links by passing them to site A which in turn 301 redirects to your site... and adding even more to the bag, go for https and throw some links that way too (make sure to canonicalize) lol....

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