This work investigates the refraction of singularities in thin parabolic elastic shells with developable mid-surfaces in the presence of rigid folds. As the shell thickness ε tends to zero, the limiting problem (ε=0) exhibits singularities that propagate along asymptotic curves, also known as characteristic curves. When these singularities encounter a fold with prescribed transmission conditions, they pass through and continue propagating on the opposite side without loss of regularity but with a change in amplitude. A theoretical framework is developed to analyze this phenomenon, supported by numerical simulations illustrating the refraction process. The results provide new insights into wave propagation and structural behavior in thin elastic shells with geometric discontinuities, which could have implications for engineering applications involving folded structures.