A quick look at the source of the extension shows they use the following addresses for gathering data and publishing 'offers':

   https://abtests.cliqz.com
   https://anolysis-gid.cliqz.com
   https://anolysis-telemetry.cliqz.com
   https://antiphishing.cliqz.com
   https://anti-tracking.cliqz.com
   https://api.cliqz.com
   https://cdn.cliqz.com
   https://cliqz.com
   https://hpn-collector.cliqz.com
   https://hpn-sign.cliqz.com
   https://offers-api.cliqz.com
   https://safe-browsing.cliqz.com
   https://safe-browsing-quorum.cliqz.com
   https://stats.cliqz.com

These can be added to the blocklist on the router or just watched for fun and profit, your choice.

As an aside, both the domain name 'cliqz.com' as well as the use of terms like 'offers' leave a bad taste. If this is really meant to be a legitimate operation they could have done better than to copy the language of the bottom feeders of the 'net, now they just come across like a revamp of 'Bonzi Buddy' and its ilk, watching users' browsing habits to provide 'shopping opportunities' and such drivel.