Addendum to: "An expansion of the Jones representation of genus 2 and the Torelli group"

We observe that the determinant of the representation provides a little restriction for the structure of the graded quotients ${\mathcal{G}}_k^{Q}F$ introduced in both [Algebr. Geom. Topol. 1 (2001) 39-55] and [J. Knot Theory Ramifications 13 (2004) 297-306] that any one of them does not contain the trivial 1-dimensional summand.