Heteroepitaxial growth of 2% lattice-mismatched EuTe on PbTe(111) by molecular beam epitaxy is investigated in the two-dimensional layer-by-layer growth regime (Frank van der Merwe growth mode) combining scanning tunnelling microscopy and in-situ reflection high-energy electron diffraction. The injection of misfit dislocation at the critical thickness of the epitaxial layer causes the appearance of monolayer step lines on the surface along certain crystallographic directions. These are formed by the glide of the grown-in threading dislocations in the layer at the onset of strain relaxation according to the (100) [110] and, among others, the ((3) over bar (1) over bar 1) [110] glide systems. Because of the initially very sluggish strain relaxation process, at first the epitaxial growth is not influenced by the formation of the surface step lines. However, at a layer thickness of 40 ML the strain relaxation rate strongly increases due to high excess stress in the layer and a dense network of surface step lines is formed, resulting in an abrupt surface roughening transition with an increase of the root mean square roughness by a factor of four.