What is the significance of the scene when Phoebe gives Holden his hunting hat back in The Catcher in the Rye?

Holden's bright red hunting hat is a vivid expression of his unique personality. In common with most young adults, he wants to proclaim his individuality, and wearing the big old hunting hat allows him to do precisely that. He wants to stand out from the crowd, to look completely different from others of his age. And to Holden, the bright red hunting hat is a sign of his authenticity, setting him apart from all the "phonies" by which he's constantly surrounded. Most important of all, the hat is a kind of comfort blanket, something that Holden feels gives him protection from a world he neither likes nor understands.
In giving the hat to Phoebe towards the end of the book, Holden is showing his concern for her well-being. He is offering his sister a symbol of childhood and the relative safety and security that it embodies. Holden is concerned at the potentially difficult transition to young adulthood that Phoebe may encounter. His own experiences in this regard form the basis of the entire book, and the last thing he wants is for Phoebe to have to go through a similar upheaval.
But he needn't worry. She's already much more mature than Holden in most respects, so she really doesn't need his hat. Throwing the floppy red hunting hat back at her brother is Phoebe's way of telling Holden that she's going to be just fine.