Using coaxial impact collision ion scattering spectroscopy, scanning tunneling microscopy (STM), and low-energy electron diffraction techniques, we have investigated the interaction of atomic hydrogen with the Si(001) 4x3-In surface phase. During this interaction, Si-In bonds are broken and replaced by SI-H bonds. As a result, the 4x3 reconstruction is destroyed and In atoms form small clusters on the hydrogen-terminated Si(001) surface. The indium clusters are found to be not monocrystalline but, rather, polycrystalline. This is in contrast with other metal adsorbate/Si systems such as H/Ag/Si(111), H/Pb/Si(111), and H/In/Si(111) where metal atoms are known to form epitaxial monocrystalline islands. The size of the In clusters increases with increasing substrate temperature during hydrogen exposure of the 4x3-In phase. Using STM, we have confirmed that, as a result of atomic hydrogen interaction, the Si substrate becomes bare and forms the Si(001) 4x1-H phase, indicating that the underlying Si layer in the Si(001) 4x3-In surface phase is reconstructed with 4x1 periodicity. A structural model of the Si(001) 4x1-H surface has been proposed.