  We consider the real topological string on certain non-compact toric
Calabi-Yau three-folds X, in its physical realization describing an orientifold
of type IIA on X with an O4-plane and a single D4-brane stuck on top. The
orientifold can be regarded as a new kind of surface operator on the gauge
theory with 8 supercharges arising from the singular geometry. We use the
M-theory lift of this system to compute the real Gopakumar-Vafa invariants
(describing wrapped M2-brane BPS states) for diverse geometries. We show that
the real topological string amplitudes pick up certain signs across flop
transitions, in a well-defined pattern consistent with continuity of the real
BPS invariants. We further give some preliminary proposals of an intrinsically
gauge theoretical description of the effect of the surface operator in the
gauge theory partition function.
