  For a knot $K,$ a slope $r$ is said to be characterizing if for no other knot
$J$ does $r$-framed surgery along $J$ yield the same manifold as $r$-framed
surgery on $K.$ Applying a condition of Baker and Motegi, we show that the
knots $T_{2,2n+3}\#T_{-2,2n+1}$ have infinitely many non-characterizing slopes.
