The chi-ribbon closure conjecture for alternating links

Let $F:L_1\to L_2$ be a $\chi$-ribbon concordance, meaning a $\chi$-concordance with no index-2 critical points, and suppose that $L_2$ is an alternating link. In the knot special case, let $F:K_1\to K_2$ be a ribbon concordance and suppose that $K_2$ is an alternating knot.

Chi-ribbon closure conjecture. Then $L_1$ is an alternating link. In particular, $K_1$ is an alternating knot in the knot case.

The source presents this as a related conjecture following its classification theorem for certain ribbon $\chi$-concordances. No resolution is supplied.