Hard x-rays from laser-produced hot electrons (>10 keV) in backlit pinhole imagers can give rise to a background signal that decreases signal dynamic range in radiographs. Consequently, significant uncertainties are introduced to the measured optical depth of imaged plasmas. Past experiments have demonstrated that hard x-rays are produced when hot electrons interact with the high-Z pinhole substrate used to collimate the softer He-α x-ray source. Results are presented from recent experiments performed on the OMEGA-60 laser to further study the production of hard x-rays in the pinhole substrate and how these x-rays contribute to the background signal in radiographs. Radiographic image plates measured hard x-rays from pinhole imagers with Mo, Sn, and Ta pinhole substrates. The variation in background signal between pinhole substrates provides evidence that much of this background comes from x-rays produced in the pinhole substrate itself. A Monte Carlo electron transport code was used to model x-ray production from hot electrons interacting in the pinhole substrate, as well as to model measurements of x-rays from the irradiated side of the targets, recorded by a bremsstrahlung x-ray spectrometer. Inconsistencies in inferred hot electron distributions between the different pinhole substrate materials demonstrate that additional sources of hot electrons beyond those modeled may produce hard x-rays in the pinhole substrate.