We use new Hubble Space Telescope (HST) images of nine Green Pea galaxies (GPGs) to study their resolved structure and color. The choice of filters, F555W and F850LP, together with the redshift of the galaxies (z ∼ 0.25), minimizes the contribution of the nebular [O iii] and Hα emission lines to the broadband images. While these galaxies are typically very blue in color, our analysis reveals that it is only the dominant stellar clusters that are blue. Each GPG does clearly show the presence of at least one bright and compact star-forming region, but these are invariably superimposed on a more extended and lower surface brightness emission. Moreover, the colors of the star-forming regions are on average bluer than those of the diffuse emission, reaching up to 0.6 magnitudes bluer. Assuming that the diffuse and compact components have constant and single-burst star formation histories, respectively, the observed colors imply that the diffuse components (possibly the host galaxy of the star formation episode) have, on average, old stellar ages (>1 Gyr), while the star clusters are younger than 500 Myr. While a redder stellar component is perhaps the most plausible explanation for these results, the limitations of our current data set lead us to examine possible alternative mechanisms, particularly recombination emission processes, which are unusually prominent in systems with such strong line emission. With the available data, however, it is not possible to distinguish between these two interpretations. A substantial presence of old stars would indicate that the mechanisms allowing large escape fractions in these local galaxies may be different from those at play during the reionization epoch.