Stasinski and Voll's hyperoctahedral group factorization conjecture

Let $B_n$ be the hyperoctahedral group, let $I\subseteq [n-1]_0$, and write $I^c$ for its complement in $[n-1]_0$. For $w\in B_n$, let $l(w)$ denote its Coxeter length and $L(w)$ its odd length. Consider the two-variable polynomial

$$\sum_{w\in B_n^{I^c}} t^{l(w)}X^{L(w)}.$$

Stasinski and Voll's conjecture. The polynomial $xt+1$ divides

$$\sum_{w\in B_n^{I^c}} t^{l(w)}X^{L(w)}$$

if and only if $0\in I$.

This conjecture asks for a factorization criterion for the length-generating polynomial of parabolic quotients in the hyperoctahedral group. The source presents it as a further conjecture; its resolution is not established by the supplied context.