The atomistic structure of the tip apex plays a crucial role in performing reliable atomic-scale surface and adsorbate manipulation using scanning probe techniques. We have developed an automated extraction routine for controlled removal of single hydrogen atoms from the H:Si(100) surface. The set of atomic extraction protocols detect a variety of desorption events during scanning tunneling microscope (STM)-induced modification of the hydrogen-passivated surface. The influence of the tip state on the probability for hydrogen removal was examined by comparing the desorption efficiency for various classifications of STM topographs (rows, dimers, atoms, etc). We find that dimer-row-resolving tip apices extract hydrogen atoms most readily and reliably (and with least spurious desorption), while tip states which provide atomic resolution counter-intuitively have a lower probability for single H atom removal.