  In this paper, we give a necessary and sufficient condition for an essential
simple loop on a $2$-bridge sphere in an even Heckoid orbifold for the trivial
knot to be null-homotopic, peripheral or torsion in the orbifold. We also give
a necessary and sufficient condition for two essential simple loops on a
$2$-bridge sphere in an even Heckoid orbifold for the trivial knot to be
homotopic in the orbifold.
