We report our new analysis of Oort-cloud comet C/2020 T2 (Palomar) (T2) observed at 2.06 au from the Sun (phase angle of 28.5 deg) about two weeks before perihelion. T2 lacks a significant dust tail in scattered light, showing a strong central condensation of the coma throughout the apparition, reminiscent of so-called Manx comets. Its spectral slope of polarized light increases and decreases in the J (1.25 um) and H (1.65 um) bands, respectively, resulting in an overall negative (blue) slope (-0.31+/-0.14 % um^-1) in contrast to the red polarimetric color of active comets observed at similar geometries. The average polarization degree of T2 is 2.86+/-0.17 % for the J and 2.75+/-0.16 % for the H bands. Given that near-infrared wavelengths are sensitive to the intermediate-scale structure of cometary dust (i.e., dust aggregates), our light-scattering modeling of ballistic aggregates with different porosities and compositions shows that polarimetric properties of T2 are compatible with low-porosity (~66 %), absorbing dust aggregates with negligible ice contents on a scale of 10--100 um (density of ~652 kg m^-3). This is supported by the coma morphology of T2 which has a viable beta (the relative importance of solar radiation pressure on dust) range of <~10^-4. Secular evolution of the r-band activity of T2 from archival data reveals that the increase in its brightness accelerates around 2.4 au pre-perihelion, with its overall dust production rate ~100 times smaller than those of active Oort-cloud comets. We also found an apparent concentration of T2 and Manx comets toward ecliptic orbits. This paper underlines the heterogeneous nature of Oort-cloud comets which can be investigated in the near future with dedicated studies of their dust characteristics.