Hollow core fibers are considered as promising candidates to deliver intense temporally overlapping picosecond pulses in applications such as stimulated Raman scattering (SRS) microscopy and endoscopy because of their inherent low nonlinearity compared to solid-core silica fibers. Here we demonstrate that, contrary to prior assumptions, parasitic signals are generated in Kagomé lattice hollow core fibers. We identify the origin of the parasitic signals as an interplay between the Kerr nonlinearity of air and frequency-dependent fiber losses. Importantly, we identify the special cases of experimental parameters that are free from parasitic signals, making hollow core fibers ideal candidates for noise-free SRS microscopy and endoscopy.