  Electron-electron interactions play a critical role in many condensed matter
phenomena, and it is tempting to find a way to control them by changing the
interactions' strength. One possible approach is to place a studied system in
proximity of a metal, which induces additional screening and hence suppresses
electron interactions. Here, using devices with atomically-thin gate
dielectrics and atomically-flat metallic gates, we measure the
electron-electron scattering length in graphene and report qualitative
deviations from the standard behavior. The changes induced by screening become
important only at gate dielectric thicknesses of a few nm, much smaller than a
typical separation between electrons. Our theoretical analysis agrees well with
the scattering rates extracted from measurements of electron viscosity in
monolayer graphene and of umklapp electron-electron scattering in graphene
superlattices. The results provide a guidance for future attempts to achieve
proximity screening of many-body phenomena in two-dimensional systems.
