  In scalar-valued Hardy space, the class of Schmidt subspaces for a bounded
Hankel operator are closely related to nearly $S^*$-invariant subspaces, as
described by G\'{e}rard and Pushnitski. In this article, we prove that these
subspaces in the context of vector-valued Hardy spaces are nearly
$S^*$-invariant with finite defect in general. As a consequence, we obtain a
short proof of the characterization results concerning the Schmidt subspaces in
scalar-valued Hardy space in an alternative way. Thus, our work complements the
work of G\'{e}rard and Pushnitski regarding the structure of Schmidt subspaces.
