Eliza's returning the ring to Higgins is a sign that she's no longer prepared to be controlled by him. Feeling used, not to mention fearful of what her uncertain future might bring, she has nothing left but her few remaining shreds of dignity. Whatever Higgins may think, Eliza's a human being in her own right, with all that that entails.
Giving Higgins back his ring is one of the few ways left open to her of reestablishing some measure of control over a life which for the duration of this "experiment" wasn't hers. Though Eliza's worried about the very real prospect of returning to the gutter, at the very least she'll be her own woman again, warts and all. But before that can happen, she wants to make sure that she has nothing in her possession that reminds her of her status as Higgins's guinea pig. With that in mind,...
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she gives him back his ring.
I would want to argue that this important scene at the end of Act IV is linked in to the wider and more far-reaching trasformations that have occurred in Eliza. Higgins is of course only focused on and aware of the external transformation, which is the source of his bet. Having succeeded in transforming a flower lady to a duchess, he is blind to the other transformations that have transpired within Eliza. Eliza here clearly shows the independent spirit that she now has. Her returning the ring that was bought for her by Higgins in Brighton symbolises the way that she refuses to be objectified and treated like a project by Higgins anymore, and demands to be able to relate to him like another human being that is his equal. Note what she says and the way that the stage directions indicate that Higgins responds to this challenge:
This ring isn't the jeweler's; it's the one you bought me in Brighton. I don't want it now. [Higgins dashes the ring violently into the fireplace, and turns on her so threateningly that she crouches over the piano with her hands over her face, and exclaims] Don't you hit me.
It is clear from his response that Higgins is aware of the symbolic meaning of her action. She is challenging the way that he thinks of her and the way that he is treated her, and trying to get him to see, as he is forced to concede in the next Act, that dignity and self-worth are not a matter of outward trappings, but of how you treat others.