As a continuation of the work by Granvik et al. (2012), we expand the statistical treatment of Earth's temporarily-captured natural satellites from temporarily-captured orbiters (TCOs, i.e., objects which make at least one orbit around the Earth) to the newly redefined subpopulation of temporarily-captured flybys (TCFs). TCFs are objects that while being gravitationally bound fail to make a complete orbit around the Earth while on a geocentric orbit, but nevertheless approach the Earth within its Hill radius. We follow the trajectories of massless test asteroids through the Earth-Moon system and record the orbital characteristics of those that are temporarily captured. We then carry out a steady-state analysis utilizing the novel NEO population model by Granvik et al. (2016). We also investigate how an quadratic distribution at very small values of e☉ and i☉ affects the predicted population statistics of Earth's temporarily-captured natural satellites. The steady-state population in both cases (constant and quadratic number distributions inside the e and i bins) is predicted to contain a slightly reduced number of meter-sized asteroids compared to the values of the previous paper. For the combined TCO/TCF population, we find the largest body constantly present on a geocentric orbit to be on the order of 80 cm in diameter. In the phase space, where the capture is possible, the capture efficiency of TCOs and TCFs is O(10-6 -10-4) . We also find that kilometer-scale asteroids are captured once every 10 Myr.