The Hubble Ultra Deep Field source JD2 presented in Mobasher et al. is an unusual galaxy that is very faint at all wavelengths shortward of 1.1 μm. Photometric redshift fits to data between 0.4 and 8 μm yield a significant probability that it is an extremely massive galaxy at z ~ 6.5. In this paper we present new photometry at 16 and 22 μm from Spitzer Infrared Spectrograph (IRS) peak-up imaging of the Great Observatories Origins Deep Survey (GOODS) fields. We find that the spectral energy distribution shows a factor of ~4 rise in flux density between the 16 and 22 μm bandpass, which is most likely due to the entrance of polycyclic aromatic hydrocarbon emission features into the 22 and 24 μm passbands. The flux ratio between these bandpasses can be best fit by a z = 1.7 luminous infrared galaxy with a bolometric luminosity of (2-6) × 10^(11) L_⊙ corresponding to a star formation rate of 80 M_⊙ yr^(-1). The predicted flux density values at other longer wavelengths are below the detection limits of current instrumentation, but such sources could potentially be detected in lensed submillimeter surveys. Reevaluation of the optical/near-infrared photometry continues to favor z > 6 photometric redshift solutions, but we argue that the consistency of the multiwavelength parameters of this galaxy with other dusty starbursts favor the z ~ 2 mid-infrared photometric redshift. The data presented here provide evidence that optically undetected near-infrared sources that are detected at 24 μm are most likely dusty, starburst galaxies at a redshift of z ~ 2 with stellar masses >10^(10) M_⊙
