Background: It is generally acknowledged that the time-dependent Hartree-Fock (TDHF) method provides a useful foundation for a fully microscopic many-body theory of low-energy heavy-ion reactions. The TDHF method is also known in nuclear physics in the small amplitude domain, where it provides a useful description of collective states, and is based on the mean-field formalism which has been a relatively successful approximation to the nuclear many-body problem. Currently, the TDHF theory is being widely used in the study of fusion excitation functions, fission, deep-inelastic scattering of heavy mass systems, while providing a natural foundation for many other studies.Purpose: With the advancement of computational power it is now possible to undertake TDHF calculations without any symmetry assumptions and incorporate the major strides made by the nuclear structure community in improving the energy density functionals used in these calculations. In particular, time-odd and tensor terms in these functionals are naturally present during the dynamical evolution, while being absent or minimally important for most static calculations. The parameters of these terms are determined by the requirement of Galilean invariance or local gauge invariance but their significance for the reaction dynamics have not been fully studied. This work addresses this question with emphasis on the tensor force. Method:The full version of the Skyrme force, including terms arising only from the Skyrme tensor force, is applied to the study of collisions within a completely symmetry-unrestricted TDHF implementation. Results:We examine the effect on upper fusion thresholds with and without the tensor force terms and find an effect on the fusion threshold energy of the order several MeV. Details of the distribution of the energy within terms in the energy density functional is also discussed.Conclusions: Terms in the energy density functional linked to the tensor force can play a non-negligible role in dynamic processes in nuclei.