Hello from South Jersey

Hello,
Amy from South Jersey. Just found you all today! Was searching StewMac to find this piece which fell off. But no idea what it is or how to fix it. To me, it this missing piece deadens the tone, though it may have nothing to do with it! Any suggestions for this Rookie? image11|666x500

Not entirely sure what this might be, are you referring to the black line that looks like fretboard binding?