Sparsity of rational points on torsion level covers of Hilbert modular varieties

Let $F$ be a totally real field of degree $n$ and discriminant $Δ_F$, and let $X_1(η)$ be the cover of the Hilbert modular variety parametrizing abelian varieties with real multiplication by $\mathcal O_F$, together with a torsion point having annihilator $η$. Let $L=K_{\overline X_1(η)}+D$ be the l