We evaluate the relationship between the hard X-ray photon spectrum and the flux of iron Kc~ emission in a thick-target electron bombardment model. Results are presented for various power-law hard X-ray spectra. We then apply these results to two events observed with the Hard X-Ray Burst Spectrometer and the Ks channel of the X-Ray Polychromator Bent Crystal Spectrometer on the Solar Maximum Mission satellite. For one of the events, on 29 March, 1980, at 09:18 UT, the Kc~ flux predicted for a thick-target non-thermal process is significant compared to the background fluorescent component, and the data are indeed consistent with an enhancement of the predicted amount. For the other event, on 14 October, 1980 at 06:09 UT, the hard X-ray spectrum is so steep that no significant Kc~ flux is predicted for this process, and no enhancement is seen. We conclude that the agreement between the predicted Kc~ flux and the observed magnitude of the Ka enhancement above the fluorescent background at the time of the large hard X-ray bursts lends support to a thick-target non-thermal interpretation of impulsive hard X-ray emission in solar flares.