  We show the following for every sufficiently connected graph $G$, any vertex
subset $S$ of $G$, and given integer $k$: there are $k$ disjoint odd cycles in
$G$ each containing a vertex of $S$ or there is set $X$ of at most $2k-2$
vertices such that $G-X$ does not contain any odd cycle that contains a vertex
of $S$. We prove this via an extension of Kawarabayashi and Reed's result about
parity-$k$-linked graphs (Combinatorica 29, 215-225). From this result it is
easy to deduce several other well known results about the Erd\H{o}s-P\'osa
property of odd cycles in highly connected graphs. This strengthens results due
to Thomassen (Combinatorica 21, 321-333), and Rautenbach and Reed
(Combinatorica 21, 267-278), respectively.
