This book has received more recognition than it deserves. Or This book has received more recognition than it has earned.

Sentence #1 is correct in my opinion. No changes needed. Sentence #2 is a bit awkward and overly complicated. I'd go with something like: "The reputation of this book is greater than it deserves." Or, perhaps (changing the word order): "This book has earned a far greater reputation than it deserves." Or (one more option): "The stature of this book far exceeds its quality." (Note I used "stature" in place of "status").

This book has gotten far more recognition than it deserves.

Without context, both are a little vague and don’t say much. The words ‘recognition’ and ‘literary status’ suggest that it has won some kind of awards, but otherwise aren’t very descriptive. Sample statements: This book’s good reputation is undeserved in my opinion. That this book was awarded the Nobel prize is a travesty. This book is highly esteemed by many English professors, but generally hated by their students. This book is receiving a lot of buzz, but I think it’s uninteresting and poorly written.