Chi-boundedness conjecture for graphs of bounded induced matching treewidth

Let $k,c\in\mathbb{N}$. Consider graphs whose induced matching treewidth is at most $k$, and write $\omega(G)$ and $\chi(G)$ for their clique and chromatic numbers, respectively.

Chi-boundedness conjecture. For any two integers $k,c\in\mathbb{N}$ there exists an integer $r$ such that every graph with induced matching treewidth at most $k$ and clique number at most $c$ has chromatic number at most $r$.

This proposes that bounded induced matching treewidth defines a $\chi$-bounded graph class, analogous to $(\operatorname{tw},\omega)$-boundedness. The assertion is stated as an open direction in the paper.