Quantum oscillations of the electron-phonon coupling of a Shockley surface state induced by the coupling to a metallic quantum well are observed experimentally as the thickness of the quantum well is increased. Microscopic calculations allow us to assign these oscillations to changes in the Eliashberg function, caused by a modulation in the electronic density overlap between the 2D surface state band and the 2D electron system of the quantum well and by the gradient of the one-electron potential in combination with the localized character of the Shockley-type surface state wave function. The findings are important in the context of the control of surface processes such as film growth and surface chemical reactions.