Aside from flat-out removing the package as the AC suggested, there's more than likely an easy way to disable it in system settings.
If my Grandmother cared enough about her privacy that she didn't want searches to show Amazon shopping results, she probably would Google how to turn it off. She's not the most tech saavy, but Google isn't *that* hard to use. Also, if she were using Ubuntu it would probably be on a system I set up for her, and not one she did herself.
Do you routinely run local searches in Ubuntu's GUI for whatever depraved porn you have? Do you include PII as search terms? No? Then whatever you are searching for probably isn't anything that really matters in terms of Amazon knowing more about you ("resume.docx" This guy must want resume writing software! or maybe Microsoft Word! Oh, wait this is Linux.... He can't use any software we sell.... Hmmm.... Maybe sell him a printer and some resume paper? Yeah, that's the ticket!).
The point is that it's not permanent, it can be removed/disabled, AND it's not really any more invasive than your average Google Search.