We present x-ray powder diffraction (XRPD) and neutron-diffraction measurements on the slightly underdoped iron-pnictide superconductor Ba1-xKxFe2As2, T-c=32 K. Below the magnetic-transition temperature T-m=70 K, both techniques show an additional broadening of the nuclear Bragg peaks, suggesting a weak structural phase transition. However, macroscopically the system does not break its tetragonal symmetry down to 15 K. Instead, XRPD patterns at low temperature reveal an increase in the anisotropic microstrain proportionally in all directions. We associate this effect with the electronic phase separation previously observed in the same material and with the effect of lattice softening below the magnetic phase transition. We employ density-functional theory to evaluate the distribution of atomic positions in the presence of dopant atoms both in the normal and magnetic states and to quantify the lattice softening, showing that it can account for a major part of the observed increase in the microstrain.