  In a paper published by the Annales de la Facult\'e de Sciences de Toulouse,
with Yousuke Ohyama, we defined and studied a space of monodromy data
underlying the well known derivation of q-Painlev\'e VI equation from
q-isomonodromy conditions by Jimbo and Sakai. In a recent ArXiv preprint,
Nalini Joshi and Pieter Roffelsen pursued our work. However, both our article
and their preprint are ambiguous on some foundational algebro-geometric
matters. We proceed here to provide sound bases.
