As of now, you can see that the banner is structured as a template WTL_Intro and it's used in the main page with some html tags and bootstrap classes see here. If you want to modify it I suggest to copy the code of the template and test it on a local environment or into the user page

My opinion is that this banner should be totally changed with a new one

I think that is better to start with a new promotional text for:
http://it.wikitolearn.org/
http://en.wikitolearn.org/

And next we can discuss about the new one.

Original english version:

WikiToLearn wants to provide free, collaborative and accessible text books to the whole world.
Our philosophy is synthetized in the sentence: “knowledge only grows if shared”. We provide a platform where learners and teachers can together complete, refine and re-assemble notes, lecture notes in order to create text books, tailored precisely to their needs, so that you can “stand on the shoulders of giants”.

So my proposal for the english version:

WikiToLearn means free, collaborative and accessible text books to the whole students world's.
Our platform lives under the term “knowledge only grows if shared”.
You can meet learners and teachers that work together on notes or on text books based from their real needs or experience.
Prepare to get an amazing vote on your next exam!