In this article we show no Dehn surgery on nontrivial strongly invertible knots can yield the lens space
L
(
2
p
,
1
)
L(2p,1)
for any integer
p
p
. In order to do that, we determine band attaches to
(
2
,
2
p
)
(2,2p)
-torus links producing the trivial knot.