  The relative photometric calibration errors in the DESI Legacy Imaging
Surveys (LS), which are used for DESI target selection, can leave imprints on
the DESI target densities and bias the resulting cosmological measurements. We
characterize the LS calibration systematics by comparing the LS stellar
photometry with Gaia DR3 synthetic photometry. We find the stellar photometry
of LS DR9 and Gaia has an \textsc{rms} difference of 4.7, 3.7, 4.4 mmag in
DECam $grz$ bands, respectively, when averaged over an angular scale of 27
arcmin. There are distinct spatial patterns in the photometric offset
resembling the Gaia scan patterns (most notably in the synthesized $g$-band)
which indicate systematics in the Gaia spectrophotometry, as well as honeycomb
patterns due to LS calibration systematics. We also find large and smoothly
varying photometric offsets at $\mathrm{Dec}<-29.25^{\circ}$ in LS DR9 which
are fixed in DR10.
