The folding model analysis of the elastic alpha + alpha scattering at the incident energies below the reaction threshold of 34.7 Me V (in the lab system) has been done using the well-tested density dependent versions of the M3Y interaction and realistic choices for the 4He density. Because the absorption is negligible at the energies below the reaction threshold, the authors were able to probe the alpha + alpha optical potential at low energies quite unambiguously and found that the alpha + alpha overlap density used to construct the density dependence of the M3Y interaction is strongly distorted by the Pauli blocking. This result gives possible explanation of a long-standing inconsistency of the double-folding model in its study of the elastic alpha + alpha and alpha-nucleus scattering at low energies using the same realistic density dependent M3Y interaction.