  Stars on eccentric orbits around a massive black hole (MBH) emit bursts of
gravitational waves (GWs) at periapse. Such events may be directly resolvable
in the Galactic centre. However, if the star does not spiral in, the emitted
GWs are not resolvable for extra-galactic MBHs, but constitute a source of
background noise. We estimate the power spectrum of this extreme mass ratio
burst background (EMBB) and compare it to the anticipated instrumental noise of
the Laser Interferometer Space Antenna (LISA). To this end, we model the
regions close to a MBH, accounting for mass-segregation, and for processes that
limit the presence of stars close to the MBH, such as GW inspiral and
hydrodynamical collisions between stars. We find that the EMBB is dominated by
GW bursts from stellar mass black holes, and the magnitude of the noise
spectrum (f S_GW)^{1/2} is at least a factor ~10 smaller than the instrumental
noise. As an additional result of our analysis, we show that LISA is unlikely
to detect relativistic bursts in the Galactic centre.
