We apply a Fourier filtering technique for the global removal of coherent contributions, like perturbed free-induction decay, and noise, to experimental pump-probe spectra. A further filtering scheme gains access to spectra otherwise only recordable by scanning the probe's center frequency with adjustable spectral resolution. These methods cleanse pump-probe data and allow improved visualization and simpler analysis of the contained dynamics. We demonstrate these filters using visible pump/mid-infrared probe spectroscopy of ligand dissociation in carboxyhemoglobin.