We report systematic studies of the transverse nuclear spin-spin relaxation times T2 of HD impurities in solid H2. The experimental results indicate three different temperature regimes: (1) an exponential temperature dependence at high temperatures, (2) a minimum in T2 for 7 K < T < 11 K, and (3) an approximately temperature-independent region for 1.5 K < T < 7 K. The latter is attributed to the quantum diffusion of the impurities at low temperatures. At very low temperatures (0.10 K < T < 1.5 K), T2 increases approximately linearly with temperature. This is attributed to the formation of bound ortho-H2 pairs. The behavior in the intermediate-temperature regime is analyzed in terms of vacancy-impurity scattering with quantum tunneling of vacancies.