The Parker Solar Probe (PSP) spacecraft has flown into the densest, previously unexplored, innermost region of our solar system's zodiacal cloud. While PSP does not have a dedicated dust detector, multiple instruments on the spacecraft are sensitive to the effects of meteoroid bombardment. Here, we discuss measurements taken during PSP's second orbit and compare them to models of the zodiacal cloud's dust distribution. Comparing the radial impact rate trends and the timing and location of a dust impact to an energetic particle detector, we find the impactor population to be consistent with dust grains on hyperbolic orbits escaping the solar system. Assuming PSP's impact environment is dominated by hyperbolic impactors, the total quantity of dust ejected from our solar system is estimated to be 0.5− 10 tons/s. We expect PSP will encounter an increasingly intense impactor environment as its perihelion distance and semimajor axis are decreased.