In this technical note, we review the computations which led to the tolerances on residual quadrupole field terms in the magnets of the Gun-To-Linac region of the LCLS Injector. If the dipole terms can be cancelled by appropriately steering the beam, the quadrupole term damages the focusing scheme and generates an asymmetry in the horizontal and vertical emittances. Quadrupole terms deteriorate the emittance compensation process and thus would prevent us from reaching the low emittance requirement of 1mm-mrad projected emittance and 0.9 mmmrad for the 80%-emittance for a 1nC bunch charge. Show Partial Abstract