Jaikin-Zapirain's profinite conciseness conjecture

Let $w$ be a group-word and $G$ a profinite group. Suppose that the set of $w$-values in $G$ is countable. Profinite conciseness conjecture. Then the verbal subgroup $w(G)$ is finite. The paper presents this as a conjecture in the context of relaxing the usual definition of conciseness for profinite groups; no resolution is given.