Matching-deletion conjecture for critical graph dimension

Let $G$ be a critical graph (not banned), let $M$ be a maximal matching, and suppose that its orthogonal representation dimension satisfies $\rho ^\text{\perp}(G)=d$. The matching-deletion conjecture. The graph obtained by deleting the matching satisfies

$$\rho ^\text{\perp}(G-M(G))\le d-1.$$

The source provides no proof or resolution.