  In a recent article [5], the authors claim that the distance between the
b-chromatic index of a tree and a known upper bound is at most 1. At the same
time, in [7] the authors claim to be able to construct a tree where this
difference is bigger than 1. However, the given example was disconnected, i.e.,
actually consisted of a forest. Here, we slightly modify their construction in
order to produce trees, thus getting that indeed the difference between the
b-chromatic index of trees and the known upper bound can be arbitrarily large.
We also point out the mistake made in [5].
