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

A note on odd reflections of super Yangian and Bethe ansatz