On ambiguities of sign determination of the S-matrix from energy levels in a finite box

In a recent paper the authors make a study on the determination of the S-matrix elements for scattering of particles in the infinite volume from the energy levels in the finite box for the case of multiple channels. The study is done with a toy model in 1+1 dimension and the authors find that there is some ambiguity in the sign of nondiagonal matrix elements, casting doubts on whether the needed observables in the infinite volume can be obtained from the energy levels of the box. In this paper I present an easy derivation, confirming the ambiguity of the sign and argue that this, however, does not put restrictions in the determination of observables.