We investigate carrier capture processes in strain-induced quantum dot structures. The quantum dots consist of a near-surface InGaAs/GaAs quantum well in which a lateral confining potential is generated by the strain from InP stressor islands grown on the sample surface. Using photoluminescence spectroscopy, we show that the rate of carrier capture into the quantum dots increases dramatically when the energetic depth of the confinement potential is reduced by enlarging the quantum well/surface separation D. While carriers in the quantum well region between the quantum dots are found to experience D-dependent nonradiative surface recombination, this process seems to be negligible for carriers in the quantum dots, presumably due to the protecting InP islands.