  The global total-$f$ gyrokinetic particle-in-cell code XGC, used to study
transport in magnetic fusion plasmas, implements a continuum grid to perform
the dissipative operations, such as plasma collisions. To transfer the
distribution function between marker particles and a rectangular velocity-space
grid, XGC employs a bilinear mapping. The conservation of particle density and
momentum is accurate enough in this bilinear operation, but the error in the
particle energy conservation can become undesirably large in special
conditions. In the present work we update XGC to use a novel mapping technique,
based on the calculation of a pseudo-inverse, to exactly preserve moments up to
the order of the discretization space. We describe the details of the
implementation and we demonstrate the reduced interpolation error for a
neoclassical tokamak test case by using $1^{\mathrm{st}}$- and
$2^{\mathrm{nd}}$-order elements with the pseudo-inverse method and comparing
to the bilinear mapping.
