  The Kerr-Schild version of the Schwarzschild metric contains a Minkowski
background which provides a definition of a boosted black hole. There are two
Kerr-Schild versions corresponding to ingoing or outgoing principle null
directions. We show that the two corresponding Minkowski backgrounds and their
associated boosts have an unexpected difference. We analyze this difference and
discuss the implications in the nonlinear regime for the gravitational memory
effect resulting from the ejection of massive particles from an isolated
system. We show that the nonlinear effect agrees with the linearized result
based upon the retarded Green function only if the velocity of the ejected
particle corresponds to a boost symmetry of the ingoing Minkowski background. A
boost with respect to the outgoing Minkowski background is inconsistent with
the absence of ingoing radiation from past null infinity.
