We actually don't even really know if Greta is the real name of the blonde, abused woman Amy meets at the Hide-A-Way cabins. Amy thinks it "sounds made up" (36.32) when she introduces herself the day they meet at the pool, but then, this is her first time on the run using a fake name, so we can't really trust her judgment.
Greta is Amy's first big mistake that brings down her formerly airtight plan. Amy initially befriends her so she can continue her pattern of having someone to control, but the irony is that Greta eventually gains control of her. Oops.
For one thing, there's a very real possibility that Greta puts two and two together and realizes who Amy really is. For instance, they start watching the Ellen Abbott coverage together, and Greta says, "'It'd be nice to think that maybe she got away […] and she's hiding out all safe and sound'" (37.107)—this comment is enough to make Amy think that just maybe, Greta knows the truth.
Or maybe, in reality, Greta doesn't know. Maybe at first she's just a girl on the run from a bad relationship looking for solidarity with other women, and it's the entrance of Jeff into their girls' club that ignites the plot to take advantage of Amy. As with many characters in Gone Girl, Greta's true motivations are tough to decipher.
Regardless of her motives, though, Greta plays a significant role in Amy's undoing. She's Jeff's accomplice in robbing Amy, and we can only imagine the secret meetings where they put this plan into motion, comparing notes about Amy's fake stories while plotting to confront and attack her. Whether Greta's been playing the role of a battered woman or not, she's played Amy for a fool and isn't afraid to be aggressive about it. Amy's totally stunned when Greta "pulls up [her] dress" and "yanks off the money belt" (40.74), before physically assaulting her.
But why put another manipulative woman in a story that's already got way too many? For one thing, we get the satisfaction of seeing someone beat Amy at her own game. For another, without the attack from Greta, Amy doesn't go to Desi's and the story doesn't continue…