It's like that special time of the month came and then never left...

Huh, didn't these girls say they surpassed the Marriage system by willpower alone? Why do I see rings on Nagato and Akagi then? (Nui's hand appears to be hidden by Nui's shouting)

They swore themselves to her in post #1926081
Since Nagato literally carved it into her finger, her ring could just be scar tissue...which would be pretty damn badass.

I post post #1926081 they unilaterally "married" (swore absolute loyalty to) Ms Katherine and carved the ring. What you see is the scar...

Apparently it works as marring the admiral in the classic romantic fashion.