A Torelli theorem for moduli spaces of parabolic vector bundles over an elliptic curve

Let $C$ be an elliptic curve, $w\in C$, and let $S\subset C$ be a finite subset of cardinality at least $3$. We prove a Torelli type theorem for the moduli space of rank two parabolic vector bundles with determinant line bundle ${\mathcal{O}}_C(w)$ over $(C,S)$ which are semistable with respect to a weight vector $(\frac{1}{2},\dots ,\frac{1}{2})$.