It was shown recently that in the submonolayer regime the shape of islands of exchanged adatoms can be changed substantially by temperature, deposition flux, or coverage in the surfactant-mediated heteroepitaxial growth systems. The shape transition from fractal islands to compact ones can be induced by decreasing temperature or increasing flux. This shape transition is completely contrary to the classic diffusion-limited aggregate (DLA) theory, but can be explained in the frame of a reaction-limited aggregate (RLA) model, in which a stable island consists of the exchanged (or dead) adatoms only, an adatom must overcome a large energy barrier to become the seed of a stable island, or overcome another little smaller barrier to join an existing island. We propose that the strain due to the mismatch in the heteroepitaxy plays the key role in the coverage-induced shape change. Our simulation shows that the strain always makes the islands more compact. With the strain taken into account, there is indeed an island shape change to more compact islands. Applied to the growth of Ge on the Si(111) substrate pre-covered by a monolayer of Pb, the coverage-induced shape change of Ge islands can be explained.