Eccentric giant planets are predicted to have acquired their eccentricity through two major mechanisms: the Kozai-Lidov effect or planet-planet scattering, but it is normally difficult to separate the two mechanisms and determine the true eccentricity origin for a given system. In this work, we focus on a sample of 92 transiting, long-period giant planets (TLGs) as part of an eccentricity distribution study for this planet population in order to understand their eccentricity origin. Using archival high-contrast imaging observations, public stellar catalogs, precise Gaia astrometry, and the NASA Exoplanet Archive database, we explored the eccentricity distribution correlation with different planet and host-star properties of our sample. We also homogeneously characterized the basic stellar properties for all 86 host-stars in our sample, including stellar age and metallicity. We found a correlation between eccentricity and stellar metallicity, where lower-metallicity stars ([Fe/H]<=0.1) did not host any planets beyond e>0.4, while higher-metallicity stars hosted planets across the entire eccentricity range. Interestingly, we found no correlation between the eccentricity distribution and the presence of stellar companions, indicating that planet-planet scattering is likely a more dominant mechanism than the Kozai-Lidov effect for TLGs. This is further supported by an anti-correlation trend found between planet multiplicity and eccentricity, as well as a lack of strong tidal dissipation effects for planets in our sample, which favor planet-planet scattering scenarios for the eccentricity origin.