  The gravitational memory effect leads to a net displacement in the relative
positions of test particles. This memory is related to the change in the strain
of the gravitational radiation field between infinite past and infinite future
retarded times. There are three known sources of the memory effect: (i) the
loss of energy to future null infinity by massless fields or particles, (ii)
the ejection of massive particles to infinity from a bound system and (iii)
homogeneous, source-free gravitational waves. In the context of linearized
theory, we show that asymptotic conditions controlling these known sources of
the gravitational memory effect rule out any other possible sources with
physically reasonable stress-energy tensors. Except for the source-free
gravitational waves, the two other known sources produce gravitational memory
with E-mode radiation strain, characterized by a certain curl-free sky pattern
of their polarization. Thus our results show that the only known source of
B-mode gravitational memory is of primordial origin, corresponding in the
linearized theory to a homogeneous wave entering from past null infinity.
