Lead quantum wells (QW) epitaxially grown on annealed Pb/Si(111) interface form a model system for the study of interactions between quantized electrons and adiabatically modulated boundaries. Tunnel spectra of this system reveal a previously unknown adiabatic shift of QW resonances due to lateral variations of the electronic reflection phase at the buried interface. With this effect, lateral distribution of the subsurface reflection phase can be probed, using scanning tunneling microscopy.