Finite-index subgroup conjecture for bounded nonsolvable definable subgroups of $SL_2$

Let $K$ be a $p$-adically closed field and let $H$ be a definable subgroup of $SL_2(K)$. Assume that $H$ is bounded and nonsolvable, and that $w$ does not normalize $H$. Let $\Gamma$ and $H_{\gamma,\eta,\eta}$ be as in the statement. Finite-index subgroup conjecture. Up to conjugacy, there exist $\gamma,\eta_1,\eta_2\in\Gamma$ such that $H_{\gamma,\eta,\eta}$ is a subgroup of $H$ of finite index at most $2(p-1)$ if $p\neq 2$, or at most $4$ if $p=2$. This gives a uniform finite-index description of bounded nonsolvable definable subgroups of $SL_2(K)$ under the stated non-normalization hypothesis; the supplied text does not establish whether the claim is resolved.