The equivalence of finite-path perfect matching and $\mathsf{ATR}_0$

Let $athsf{PM}$ denote the perfect matching principle, and let $ext{Finite Path }\mathsf{PM}$ denote its restriction to finite-path instances. Let $peratorname{\mathsf{ATR}}_0$ and $peratorname{\mathsf{RCA}}_0$ be the indicated systems of reverse mathematics.

Finite-path perfect matching conjecture. $ext{Finite Path }\mathsf{PM}$ is equivalent to $peratorname{\mathsf{ATR}}_0$ over $peratorname{\mathsf{RCA}}_0$.

The paper proves that finite-path perfect matching is close in strength to $peratorname{\mathsf{ATR}}_0$ and asks whether it implies that system, as well as whether $peratorname{\mathsf{ATR}}_0$ proves finite-path perfect matching or perfect matching. The supplied text does not resolve these questions.