For reference:
https://prism-break.org/en/categories/gnu-linux/#operating-systems - see the last comment, which is about Ubuntu
https://www.eff.org/deeplinks/2012/10/privacy-ubuntu-1210-amazon-ads-and-data-leaks
So, if you're not already using it, you might want to switch to the Debian based Mint and avoid the Ubuntu one.
Well its very easy to disable those searches:
http://askubuntu.com/questions/192269/how-can-i-remove-amazon-search-results-from-the-dash-or-disable-the-feature
The problem is, that is the only reported placed in which the data leaks happen; but no one knows if that is the only place where they happen. By using Ubuntu, or any other distro that is based on it, you basically have to trust them that no more information about you is being collected and sent elsewhere.
The prism-break page has a link to the discussion page in which they go into more detail about it: https://github.com/nylira/prism-break/issues/334