  Many gravitational wave (GW) sources are expected to have non-negligible
eccentricity in the millihertz band. These highly eccentric compact object
binaries may commonly serve as a progenitor stage of GW mergers, particularly
in dynamical channels where environmental perturbations bring a binary with
large initial orbital separation into a close pericenter passage, leading to
efficient GW emission and a final merger. This work examines the stochastic GW
background from highly eccentric ($e\gtrsim 0.9$), stellar-mass sources in the
mHz band. Our findings suggest that these binaries can contribute a substantial
GW power spectrum, potentially exceeding the LISA instrumental noise at $\sim
3-7$~mHz. This stochastic background is likely to be dominated by eccentric
sources within the Milky Way, thus introducing anisotropy and time dependence
in LISA's detection. However, given efficient search strategies to identify GW
transients from highly eccentric binaries, the unresolvable noise level can be
substantially lower, approaching $\sim 2$ orders of magnitude below the LISA
noise curve. Therefore, we highlight the importance of characterizing
stellar-mass GW sources with extreme eccentricity, especially their transient
GW signals in the millihertz band.
