In the dissociation of a noncovalent biomolecular bond by external pulling, the bonded site is often connected to the force-acting site by a linkage. The role of the linkage stiffness on the rupture of a ligand-receptor complex under constant force is investigated by overdamped Langevin dynamics for the elastically coupled ligand and probe. The effects on the bond lifetime include effective ligand diffusivity, force fluctuations, and violation of adiabatic condition. The rupture rate declines with increasing linkage stiffness. For soft linkage, the effect associated with the spring and probe can be ignored, and the true rupture rate can be extracted. On the other hand, for stiff linkage, the diffusivity of the probe has to be accounted for and, thus, leads to a lower rupture rate, depending on the diffusivity ratio between the probe and ligand. Nevertheless, the energy barrier height can be reasonably extracted by constant pulling experiments, regardless of the linkage stiffness.