We measure the absolute magnitude, H, distribution, dN(H) ∝ 10αH, of the scattering Trans-Neptunian Objects (TNOs) as a proxy for their size-frequency distribution. We show that the H-distribution of the scattering TNOs is not consistent with a single-slope distribution, but must transition around Hg ∼ 9 to either a knee with a shallow slope or to a divot, which is a differential drop followed by second exponential distribution. Our analysis is based on a sample of 22 scattering TNOs drawn from three different TNO surveys - the Canada-France Ecliptic Plane Survey, Alexandersen et al., and the Outer Solar System Origins Survey, all of which provide well-characterized detection thresholds - combined with a cosmogonic model for the formation of the scattering TNO population. Our measured absolute magnitude distribution result is independent of the choice of cosmogonic model. Based on our analysis, we estimate that the number of scattering TNOs is (2.4-8.3) × 105 for Hr < 12. A divot H-distribution is seen in a variety of formation scenarios and may explain several puzzles in Kuiper Belt science. We find that a divot H-distribution simultaneously explains the observed scattering TNO, Neptune Trojan, Plutino, and Centaur H-distributions while simultaneously predicting a large enough scattering TNO population to act as the sole supply of the Jupiter-Family Comets.