Gunningham [‘Spin Hurwitz numbers and topological quantum field theory’,
Geom. Topol.20(4) (2016), 1859–1907]
constructed an extended topological quantum field theory (TQFT) to obtain a
closed formula for all spin Hurwitz numbers. In this note, we use a gluing
theorem for spin Hurwitz numbers to re-prove Gunningham’s formula. We also
describe a TQFT formalism naturally induced by the gluing theorem.