In the interaction of a transversely polarized nuclear beam with a tensor-polarized deuteron target, a nonzero value of the component of the total cross section corresponding to this combination of polarizations is an unambiguous signal ofT-invariance violation whileP-parity is preserved. The method developed earlier for calculating this component of the total cross section forpdscattering based on the Glauber theory has been generalized by us to the case of3Hedscattering, and its energy dependence in the range of beam energies 0.1–1 GeV/nucleon has been calculated. It is found that in3Hedcollisions, in contrast topdscattering, the contribution of only one type ofT-violating nucleon-nucleon forces dominates, which is essential for extraction of the unknown constant of this interaction from the corresponding data.