Hybrid inorganic-organic materials such as quantum dots (QDs) coupled with organic semiconductors have a wide range of optoelectronic applications, taking advantage of the respective materials' strengths. A key area of investigation in such systems is the transfer of triplet exciton states to and from QDs, which has potential applications in the luminescent harvesting of triplet excitons generated by singlet fission, in photocatalysis and photochemical upconversion. While the transfer of energy from QDs to the triplet state of organic semiconductors has been intensely studied in recent years, the mechanism and materials parameters controlling the reverse process, triplet transfer to QDs, have not been well investigated. Here, through a combination of steady-state and time-resolved optical spectroscopy we study the mechanism and energetic dependence of triplet energy transfer from an organic ligand (TIPS-tetracene carboxylic acid) to PbS QDs. Over an energetic range spanning from exothermic (-0.3 eV) to endothermic (+0.1 eV) triplet energy transfer we find that the triplet energy transfer to the QD occurs through a single step process with a clear energy dependence that is consistent with an electron exchange mechanism as described by Marcus-Hush theory. In contrast, the reverse process, energy transfer from the QD to the triplet state of the ligand, does not show any energy dependence in the studied energy range; interestingly, a delayed formation of the triplet state occurs relative to the quantum dots' decay. Based on the energetic dependence of triplet energy transfer we also suggest design criteria for future materials systems where triplet excitons from organic semiconductors are harvested QDs, for instance in light emitting structures or the harvesting of triplet excitons generated singlet fission.