  We explore memory effects for novel Kundt wave spacetimes in the recently
proposed Eddington-inspired Born-Infeld (EiBI) theory of gravity. First, we
construct new, exact Kundt wave geometries in this theory for two different
matter sources--(i) generic matter designed to satisfy the field equations as
well as energy conditions, and (ii) electromagnetic field. For both sources we
find that the EiBI theory parameter $\kappa$ couples only with the nonradiative
part of the physical metric solution. Thereafter, we solve the geodesic and the
geodesic deviation equations, in the above spacetimes with the aim of arriving
at memory effects. This analysis is carried out numerically and reveals unique
memory features depending on the type of matter source present and the
signature of the spacetime scalar curvature. The role of $\kappa$ in
influencing the memory effect, for a given background spacetime, is also noted.
Thus, apart from providing novel radiative solutions in EiBI gravity, we also
show how different matter configurations are responsible for distinct memory
characteristics.
