  In a recent paper arXiv:2109.09462, Molev introduced analogues of the odd
reflections for the super Yangian $\mathrm{Y}(\mathfrak{gl}_{m|n})$ and
obtained a transition rule for the change of highest weights when the parity
sequence is altered. In this note, we reproduce the results from a different
point of view and discuss their relations with the fermionic reproduction
procedure of the XXX-type Bethe ansatz equations introduced in
arXiv:1811.11225. We give an algorithm that how the $q$-characters change under
the odd reflections. We also take the chance to compute explicitly the
$q$-characters of skew representations of $\mathrm{Y}(\mathfrak{gl}_{m|n})$ for
arbitrary parity sequences.
