The "New reads" is generated from her library.
Are you possibly referring to "what to read next"? I'm not positive, but I believe this list is generated from her friends selections and items similar to what she already has in her library.
To my knowledge, you can't turn either list off. You may be able to keep the list from updating by keeping Wi-Fi turned off and sideloading all purchases.
I wouldn't worry about it too much. I understand wanting it gone, but it's really just an ad. She sees far worse ads on TV. If she adds the book to her wish list, when you see it and research it you can have a meaningful discussion with her about why that particular book isn't appropriate for her age, and remove it from the list. While unfortunate, this isn't much different from going to a movie with your kids and having trailers play for movies you wouldn't find appropriate for them (the trailer is fine, but the actual movie wouldn't be). It would be nice if we had a bit more parental control and filtering over all, but as it is today the Nook devices are safe for use by kids as long as the parents control book purchases.
I understand that this is a classic book that has been around for a while and may be on a 'New Reads' due to its increase in popularity.
The main thing that actually concerns me about what you presented is that Game of Thones (book 1 of Song of Ice and Fire) has not been a Free Book in at least the last few years if at all on the ebook.
Hmmmm....that IS interesting about it not being a free book.
She has no way to pay for books online.
Now I'm VERY curious....
New Reads displays the most recent downloads to the device.
While B&N sometimes (for marketing reasons) will put items in accounts, these are usually samples, not entire books. And it does not seem to happen regularly.
What to Read Next are recommendations based on other books in the account's library and have not been downloaded yet.
She also could have downloaded a free sample of the book herself. They don't require payment, only a default CC online to authorize the DRM.
Some of the content of GoT may be a little excessive for her age. Though just about anything written in the fantasy genre post-1970 has that potential, unless it was specifically written for teens or kids.
Anne McCaffrey's Dragonriders, Terry Goodkind's Sword of Truth—to name just two famous/popular series. I'm not commentating, just pointing out that books written for adults may include adult content. Editorially, books written for teens are younger have obviously more stringent requirements for themes and actions and how (or if) they are portrayed.
From what you describe, I wouldn't come down too hard on her. Even if she did intentionally download it, say based on the description or recommendations, she obviously realized it's not for her.
GoT is actually a well done and regarded novel, but not something I would recommend as the next step up for Eragon fans. My daughter, who is a little older but still a teen, I had no problem sharing a copy with.
GoT has some depictions of violence that are meant to make you squirm. But it is certainly not for younger teens.
I'd dig further. There's something going on here...