Geelen's coarse Gallai conjecture for A-paths

Let $G$ be a finite or infinite graph and let $A\subseteq V(G)$. An $A$-path is a path in $G$ between two distinct vertices of $A$. Two subgraphs are at distance at least $r$ when the distance between their vertex sets is at least $r$. A set is $(a,b)$-centered if it is contained in the union of at most $a$ balls of radius at most $b$. Geelen's coarse Gallai conjecture. There exist functions $f,g:\mathbb N\rightarrow\mathbb R$ such that for any $k,r\in\mathbb N$, graph $G$ and $A\subseteq V(G)$, either there exist $k$ $A$-paths pairwise at distance in $G$ at least $r$, or there exists a set $(f(k),g(r))$-centered in $G$ intersecting all $A$-paths. The conjecture is a coarse version of Gallai's packing-covering theorem for $A$-paths. The source does not state a resolution; its exact original formulation was reported as lost, and this is the formulation attributed to Geelen by Hendrey and Jacobs.