  The impact of possible a-priori "imprinting" effects of general relativity
itself on recent attempts to measure the Lense-Thirring precessions with the
LAGEOS satellites orbiting the Earth and the terrestrial geopotential models by
the dedicated mission GRACE is investigated. It is analytically shown that
general relativity, not explicitly solved for in the GRACE-based models, may
"imprint" their even zonal harmonic coefficients J_L at a non-negligible level,
given the present-day accuracy in recovering them. This translates into a bias
of the LAGEOS-based relativistic tests as large as the Lense-Thirring effect
itself. Further analyses should include general relativity itself in the GRACE
data processing by explicitly solving for it.
