I don't understand how you can look at behavior like this from the companies selling these systems and conclude that it is ethical for them to do so, or for you to promote their products.
Using just a few words (the name of the team) feels OK to me, though you're welcome to argue otherwise.
The Claude search system prompt is there to ensure that Claude doesn't spit out multiple paragraphs of text from the underlying website, in a way that would discourage you from clicking through to the original source.
Personally I think this is an ethical way of designing that feature.
(Note that the way this works is an entirely different issue from the fact that these models were training on unlicensed data.)