In this article, we report classical sensing with undetected light at a wavelength of 1500 nm, detected on a silicon camera at 580 nm, using four-wave mixing from a plasmonic metasurface. The bidirectional nonlinear scattering due to inherent reflections from such thin nonlinear materials modifies their operation within a nonlinear interferometer. The theoretical model for visibility accounting for such bidirectionality as well as pulsed illumination accurately predicts visibility in the system as a function of transmission in the near-infrared seed (idler) arm. Spectrally resolving the visible signal emission evaluates the total dispersion within the interferometer, highlighting the prospect of ultrafast sensing with undetected photons.