Topological specialization conjecture for mock Alexander polynomials

Let $K$ be a knotoid diagram in $S^2$ whose tail lies in the exterior. Let $K_{\mathrm{ext}}$ be the starred knotoid diagram with a star in the exterior region of $K$, and let $K_{\mathrm{in}}$ be the starred knotoid diagram with a star in the region containing the head of $K$. The mock Alexander polynomial of a starred diagram $L$ is denoted by $\nabla_L(W)$.

Topological specialization conjecture. The two mock Alexander polynomials satisfy

$$\nabla_{K_{\mathrm{ext}}}(W)=\nabla_{K_{\mathrm{in}}}(-W^{-1}).$$

This is presented as a topological specialization of the star-placement symmetry conjecture for knotoids in $S^2$. The supplied text does not state a proof or resolution.