Alfvén wings are known to form when a conducting or mass-loading object slows down a flowing plasma in its vicinity. Alfvén wings are not expected to be generated when an inert moon such as Rhea interacts with Saturn's magnetosphere, where the plasma impacting the moon is absorbed and the magnetic flux passes unimpeded through the moon. However, in two close polar passes of Rhea, Cassini clearly observed magnetic field signatures consistent with Alfvén wings. In addition, observations from a high-inclination flyby (Distance > 100 RRh) of Rhea on 3 June 2010 showed that the Alfvén wings continue to propagate away from Rhea even at this large distance. We have performed three-dimensional hybrid simulations of Rhea's interaction with Saturn's magnetosphere which show that the wake refilling process generates a plasma density gradient directed in the direction of corotating plasma. The resulting plasma pressure gradient exerts a force directed toward Rhea and slows down the plasma streaming into the wake along field lines. As on the same field lines, outside of the wake, the plasma continues to move close to its full speed, this differential motion of plasma bends the magnetic flux tubes, generating Alfvén wings in the wake. The current system excited by the Alfvén wings transfers momentum to the wake plasma extracting it from plasma outside the wake. Our work demonstrates that Alfvén wings can be excited even when a moon does not possess a conducting exosphere.