This correspondence explores the application of sparse equalizers in generalized time-reversed space-time block codes (GTR-STBCs) for a two-transmit/one-receive antenna aeronautical telemetry link. It is shown that the jointly optimum design of the sparse equalizer coefficients and the power sharing parameter ρ in GTR-STBCs is computationally challenging because the active tap ratio of the sparse equalizers is a non-convex function of ρ. A search algorithm based on a grid search followed by an interpolation is shown to yield impressive results. Our numerical results demonstrate that depending on signal-to-noise ratio and channel conditions, the number of non-zero taps of sparse equalizers for GTR-STBCs can be reduced by 53% to 86% at the cost of 0.25 dB relaxation in the mean-squared error.