WIRC+Pol is a near-infrared low-resolution spectropolarimeter on the 200-inch Telescope at Palomar Observatory. The instrument utilizes a polarization grating to perform polarimetric beam splitting and spectral dispersion simultaneously. It can operate either with a focal plane slit to reduce sky background or in a slitless mode. Four different spectra sampling four linear polarization angles are recorded in the focal plane, allowing the instrument to measure all linear polarization states in one exposure. The instrument has been on-sky since February 2017 and we found that the systematic errors, likely arising from flat fielding and gravity effects on the instrument, limit our accuracy to ~1%. These systematic effects were slowly varying, and hence could be removed with a polarimetric modulator. A half-wave plate modulator and a linear polarizer were installed in front of WIRC+Pol in March 2019. The modulator worked as expected, allowing us to measure and remove all instrumental polarization we previously observed. The deepest integration on a bright point source (J = 7.689, unpolarized star HD65970) demonstrated uncertainties in q and u of 0.03% per spectral channel, consistent with the photon noise limit. Observations of fainter sources showed that the instrument could reach the photon noise limit for observations in the slitless mode. For observations in slit, the uncertainties were still a factor of few above the photon noise limit, likely due to slit loss.