Although the gold ring held great sentimental value to Claire despite how her marriage to Frank fell apart, it’s not so remarkable that Brianna would see it and immediately connect it to the parents who raised her.
Ronald Moore’s comments at the recent Savannah College of Art and Design Film Festival (via EW) reveal that Stephen Bonnet stole Jamie’s ring because Jamie’s ring stands out more than the plain gold band from Frank.
Honestly, the reason for the ring switcheroo is so straightforward that I’m almost disappointed!