  At linear order the only expected source of a curl-like, B mode, polarization
pattern in the cosmic microwave background (CMB) is primordial gravitational
waves. At second-order B modes are also produced from purely scalar, density,
initial conditions. Unlike B modes from primordial gravitational waves, these B
modes are expected to be non-Gaussian and not independent from the temperature
and gradient-like polarization, E mode, CMB anisotropies. We find that the
three point function between a second-order B mode and two first-order T/E
modes is a powerful probe of second-order B modes and should be detectable by
upcoming CMB experiments. We focus on the contribution to the three point
function arising from non-linear evolution and scattering processes before the
end of recombination as this provides new information on the universe at $z>
1000$. We find that this contribution can be separated from the other
contributions and is measurable at $\sim 2.5 \sigma$ by CMB experiments with
noise levels of $\sim 1 \mu$Karcmin and delensing efficiencies $\ge 90\%$, such
as the proposed PICO satellite. We show that approximately half of the total
signal arises from non-linearly induced vector and tensor metric perturbations,
as evaluated in the Newtonian gauge. This bispectrum is a unique probe of these
perturbations in the CMB, as their contribution to the power spectrum is
suppressed. An important feature of this bispectrum is that the detectability
will increase with decreasing experimental noise, in the absence of primordial
B modes, provided that delensing efficiencies improve in parallel.
