Injectivity conjecture for forgetful charts of prestable curves

Let $(g,n)\neq(1,0)$, and fix $d\geq 0$. For a prestable curve with $n+m$ markings, forgetting the last $m$ markings defines a morphism

$$F_m:\overline{\mathcal{M}}_{g,n+m}\to\mathfrak{M}_{g,n}.$$

Injectivity conjecture. There exists $m_0\geq 0$ such that, for every $m\geq m_0$, the pullback

$$F_m^*:\mathrm{CH}^d(\mathfrak{M}_{g,n})\to\mathrm{CH}^d(\overline{\mathcal{M}}_{g,n+m})$$

is injective.

The conjecture would make the Chow groups of stable-curve moduli spaces determine the Chow groups of the corresponding prestable-curve stacks. The source notes that, for sufficiently large $m$, the image of $F_m$ is open with complement of codimension $\lfloor m/2\rfloor+1$, but injectivity of the pullback remains conjectural.