We present the 250, 350, and 500 micron detection of bright submillimeter emission in the direction of the Bullet Cluster measured by the Balloon-borne Large Aperture Submillimeter Telescope (BLAST). The 500 micron centroid is coincident with an AzTEC 1.1 mm point-source detection at a position close to the peak lensing magnification produced by the cluster. However, the 250 micron and 350 micron centroids are elongated and shifted toward the south with a differential shift between bands that cannot be explained by pointing uncertainties. We therefore conclude that the BLAST detection is likely contaminated by emission from foreground galaxies associated with the Bullet Cluster. The submillimeter redshift estimate based on 250-1100 micron photometry at the position of the AzTEC source is z_phot = 2.9 (+0.6 -0.3), consistent with the infrared color redshift estimation of the most likely IRAC counterpart. These flux densities indicate an apparent far-infrared luminosity of L_FIR = 2E13 Lsun. When the amplification due to the gravitational lensing of the cluster is removed, the intrinsic far-infrared luminosity of the source is found to be L_FIR <= 10^12 Lsun, consistent with typical luminous infrared galaxies.
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