  Let $(X,D)$ and $(X',D')$ be two compact Riemann surfaces of genus $g \geq 4$
with the set of marked points $D \subset X$ and $D' \subset X'$. Fix a
parabolic line bundle $L$ with trivial parabolic structure. Let
$\mathcal{N}_{\textnormal{Sp}}(2m,\alpha,L)$ and
$\mathcal{N}'_{\textnormal{Sp}}(2m,\alpha,L)$ be the moduli spaces of stable
symplectic parabolic Higgs bundles over $X$ and $X'$ respectively, with rank
$2m$ and fixed parabolic structure $\alpha$, with the symplectic form taking
values in $L$. We prove that if $\mathcal{N}_{\textnormal{Sp}}(2m,\alpha,L)$ is
isomorphic to $\mathcal{N}'_{\textnormal{Sp}}(2m,\alpha,L)$, then there exist
an isomorphism between $X$ and $X'$ sending $D$ to $D'$.
