Many of the materials properties of high-entropy alloys (HEAs), like increased hardness, reduced thermal and electrical conductivity, and interesting hydrogen storage properties, are proposed to be related to local lattice distortions of the crystal structure due to the significant size differences between the elements of the alloy. However, direct evidence of this effect is very limited in the literature, and it therefore remains a hypothesis. This work presents a detailed assessment of the local lattice distortion in three body-centered cubic (bcc) HEAs TiVNb, TiVZrNb and TiVZrNbHf with varying atomic size differences using total scattering measurements and Reverse Monte Carlo structure modelling. The analysis indicates that the amount of local lattice distortion in the alloys increases with the elemental size difference in the alloy. The amount of lattice distortion is relieved when dideuterides with CaF2-type structures (Fm3¯m) are formed from the bcc (Im3¯m) HEAs. Analyses of the local environments around the deuterium atoms reveal an interesting correlation between the valence-electron concentration (VEC) of the nearest-neighbour metals and the stability of tetrahedral interstices with respect to deuterium occupation. Moreover, there is a tendency towards Ti/Nb short-range order in TiVNbD5.7 where the mixing entropy is lowest. In TiVZrNbHfD10, about 6 % of the deuterium atoms are displaced from the tetrahedral interstices with smaller volumes to octahedral interstices.