  In the Color Glass Condensate, the inclusive spectrum of produced quarks in a
heavy ion collision is obtained as the Fourier transform of a $2$-fermion
correlation function. Due to its non-locality, the two points of this function
must be linked by a Wilson line in order to have a gauge invariant result, but
when the quark spectrum is evaluated in a background that has a non-zero
chromo-magnetic field, this procedure suffers from an ambiguity related to the
choice of the contour defining the Wilson line. In this paper, we use an
analytically tractable toy model of the background field in order to study this
contour dependence. We show that for a straight contour, unphysical
contributions to the spectrum in $p_\perp^{-2}$ and $p_\perp^{-3}$ cancel,
leading to a spectrum with a tail in $p_\perp^{-4}$. If the contour defining
the Wilson line deviates from a straight line, the path dependence is at most
of order $p_\perp^{-5}$ if its curvature is bounded, and of order
$p_\perp^{-4}$ otherwise. When the contour is forced to go through a fixed
point, the path dependence is even larger, of order $p_\perp^{-2}$.
