I'm very confused about the rings.....

So I watched the series before ready the books. Just turned the page to Part 4: River Run and I'm so confused. In the series Bonnet took the silver ring and it was a whole thing. And Jamie got the candle sticks made into a new ring for Clair and blah blah blah whatever. But what's the deal with Franks ring? Does Jamie get her a new one made? Does Bree recognize it and that's what leads to her encounter with Bonnet? I know I just need to keep reading but I just NEED TO KNOW