We present long-slit near-infrared spectroscopic observations of six nearby (z ∼ 0.1) radio-quiet type-2 quasars (QSO2s) from the Quasar Feedback (QSOFEED) sample. The QSO2s have bolometric luminosities of 1045 − 46 erg s−1 and stellar masses of 1010.6−11.3 M⊙. The observations were obtained with the instrument Espectrógrafo Multiobjeto Infra-Rojo (EMIR) at the 10.4 m Gran Telescopio Canarias. The nuclear K-band spectra (central ∼1─3 kpc of the QSO2s) reveal signatures of high-velocity outflows in either the Paα or Brγ lines, depending on the redshift, and in the [Si VI] lines. The broadest kinematic components have a full width at half maximum (FWHM) of ∼1200─2500 km s−1. From the near-infrared hydrogen recombination lines, we derived ionized outflow masses of MHion ∼ 0.08−20 × 106 M⊙, mass outflow rates of ṀHion ∼ 0.03−6 M⊙ yr−1, and kinetic powers of ĖHion ∼ 1037.8−40.8 erg s−1. These ionized gas outflow masses and mass outflow rates have median values that are 5.9 and 5.8 times larger, respectively, than those derived from the [Si VI] line. Our study provides evidence, at least for these six QSO2s, that the near-infrared recombination lines and [Si VI] trace the same outflow (i.e., they have similar kinematics and radii), but they carry different amounts of mass. We detected warm molecular lines in the six QSO2s, from which we measured total (nuclear) gas masses from 1.1 (0.7) to 32 (13) × 103 M⊙, similar to other QSO2s with warm H2 measurements reported in the literature, but we did not find any molecular outflow associated with them. Based on comparison with five other QSO2s with H2 measurements reported in the literature, we find that the four QSO2s with detected H2 outflows have total (nuclear) H2 masses that are 2.2 (2.7) times larger, on average, than the seven QSO2s without detected H2 outflows.