A bound for twists of $\mathrm{G}{\mathrm{L}}_3\times \mathrm{G}{\mathrm{L}}_2$ $L$-functions with composite modulus

Let $\pi$ be a Hecke-Maass cusp form for $\mathrm{S}{\mathrm{L}}_3(\mathbf{Z})$ and let $g$ be a holomorphic or Maass cusp form for $\mathrm{S}{\mathrm{L}}_2(\mathbf{Z})$. Let $\chi$ be a primitive Dirichlet character of modulus $M=M_1{M}_2$ with $M_i$ prime, $i=1,2$. Suppose that $M^{1\mathrm{/}2+2\eta }<M_1<M^{1-2\eta }$ with $0<\eta <1\mathrm{/}8$. Then we have $$L(\frac{1}{2},\pi \otimes g\otimes \chi ){\ll }_{\pi ,g,\epsilon }{M}^{3\mathrm{/}2-\eta +\epsilon }\mathrm{.}$$