  For a prime $p>2$, Kisin and Pappas constructed parahoric integral models at
$p$ for Shimura varieties attached to Shimura data $(G,X)$ of abelian type such
that $G$ splits over a tamely ramified extension of $\mathbb{Q}_p$. A certain
auxiliary data has to be chosen in their constructions. In this note, we will
show that the parahoric integral models are actually independent of the choices
of the auxiliary data. We also get partial results on extending morphisms of
Shimura varieties to those of parahoric integral models.
