Conjecture on orientation reversal for even-winding satellite patterns

Let $P$ be a pattern with winding number, the algebraic intersection number of the pattern with a meridional disk of the solid torus, a nonzero even integer. For a knot $K$, write $P(K)$ for the satellite knot obtained from $P$ and $K$, and write $-K$ for the inverse of $K$ in the smooth knot concordance group. Even-winding reversal conjecture. There exists a knot $K$ such that $P(-K)$ is not concordant to $-P(K)$. No such example is known for even winding number unless the pattern induces the zero map, so the conjecture remains open.