The worm-gear-T function parametrizes the probability of finding a longitudinally polarized quark inside a transversely polarized hadron. We extract it from data on polarized semi-inclusive deep-inelastic scattering measured at COMPASS , HERMES. As a theoretical model, we use a Wandzura-Wilczek-type approximation at next-to-leading order. We find that at present, the data quality is insufficient to determine the worm-gear-T function faithfully. We also provide predictions for the transverse single-spin asymmetry associated with the worm-gear-T function, which could be measured in weak-boson production at STAR.