The bounded-composition conjecture for normalized Loewner mappings

Let $S^0(\mathcal D_n)$ be the normalized Loewner class. Suppose that $f\in S^0(\mathcal D_n)$ is bounded by $M>0$, and let $G\in S^0(\mathcal D_n)$. Bounded-composition conjecture. Then

$$MG\left(\frac{1}{M}f\right)\in S^0(\mathcal D_n).$$

This is stated as a further open problem related to the bounded-support-point conjecture.