We show that in TeV-scale left-right (L-R) symmetric seesaw models, there are new dominant contributions to the collider signals of heavy Majorana neutrinos arising from the heavy-light neutrino mixing, which directly probe the seesaw matrix in a certain class of models. We propose a way to distinguish this contribution from the widely discussed one that only probes the Majorana nature of the heavy right-handed neutrinos, by analyzing some simple kinematical variables. We find that in this class of L-R seesaw models the existing LHC data already yield slightly stronger constraints on the heavy-light neutrino mixing than those derived for standard seesaw models, and the improvement will be significant as more data are collected. ; Comment: 6 pages, 4 figures, 1 table; version accepted for publication in Phys. Rev. D