I'm on the fence here, in that I'm not a fan of Amazon or Google, but I don't
know that this is a software freedom issue. I would have a problem with the
Amazon search engine being built into the desktop environment Ubuntu-style,
as I would consider that an endorsement, but one-click search engines seem
like a reasonable feature for a web browser. Note that you are free to add
and remove search engines.
Amazon's and Google's search engines can be used without any proprietary
software if you don't allow their JavaScript, and there are reasons you might
choose to use them. For instance, while I refuse to buy from Amazon I will
use their search engine to discover books to buy from other vendors.
The fact that Google and Amazon (among other evils) create some proprietary
software doesn't necessarily mean that everything associated with them must
be avoided. There are ways in which free software benefits from Google. For
example, enough of Android is free software that it was easier to fork it to
create a mostly libre mobile OS (LineageOS) which was then forked to create
an entirely libre mobile OS (Replicant) than it would have been to create
Replicant from scratch. GNU Lilypond regularly participates in and benefits
from Google Summer of Code. Google also does harmful things, but that isn't a
reason not to take advantage of ways to benefit from them that don't
compromise our freedom. They certainly don't mind taking advantage of ways to
benefit from us!
Trisquel shouldn't actively promote these companies and certainly shouldn't
include any of their proprietary software, but I'm not sure whether
supporting their search engines is outside of Trisquel's policies.
Perhaps you should report this as an issue with the 'branding' tag just to
make sure that the developer is aware, and they'll determine whether or not
it should be removed.