Kim–Yip–Yoo's multiplicative irreducibility conjecture for shifted subgroups

Let $d\geq 2$ be fixed. Let $q\equiv 1\pmod d$ be a sufficiently large prime power, and let $G$ be the multiplicative subgroup of $\mathbb F_q$ of index $d$. For each $\lambda\in\mathbb F_q^*$, consider the shifted set $(G-\lambda)\setminus\{0\}$. Kim–Yip–Yoo's multiplicative irreducibility conjecture. For every $\lambda\in\mathbb F_q^*$, the set $(G-\lambda)\setminus\{0\}$ has no nontrivial multiplicative decomposition.