  In his PhD thesis, Goosen combined the string-net and the
generators-and-relations formalisms for arbitrary once-extended 3-dimensional
TQFTs. In this paper we work this out in detail for the simplest non-trivial
example, where the underlying spherical fusion category is the category of
$\mathbb{Z}/2\mathbb{Z}$-graded vector spaces. This allows us to give an
elementary string-net description of the linear maps associated to
3-dimensional bordisms. The string-net formalism also simplifies the
description of the mapping class group action in the resulting TQFT. We
conclude the paper by performing some example calculations from this viewpoint.
