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We analyze the behavior of the argument of pericenter $\omega_2$ of an outerparticle in the elliptical restricted three-body problem, focusing on theinverse Lidov-Kozai resonance. First, we calculate the contribution of theterms of quadrupole, octupole, and hexadecapolar order of the secularapproximation of the potential to the outer particle's $\omega_2$ precessionrate $(d\omega_2/d\tau)$. Then, we derive analytical criteria that determinethe vanishing of the $\omega_2$ quadrupole precession rate$(d\omega_2/d\tau)_{\text{quad}}$ for different values of the inner perturber'seccentricity $e_1$. Finally, we use such analytical considerations and describethe behavior of $\omega_2$ of outer particles extracted from N-bodysimulations. Our analytical study indicates that the values of the inclination$i_2$ and the ascending node longitude $\Omega_2$ associated with the outerparticle that vanish $(d\omega_2/d\tau)_{\text{quad}}$ strongly depend on theeccentricity $e_1$ of the inner perturber. In fact, if $e_1 <$ 0.25 ($>$0.40825), $(d\omega_2/d\tau)_{\text{quad}}$ is only vanished for particleswhose $\Omega_2$ circulates (librates). For $e_1$ between 0.25 and 0.40825,$(d\omega_2/d\tau)_{\text{quad}}$ can be vanished for any particle for asuitable selection of pairs ($\Omega_2$, $i_2$). Our analysis of the N-bodysimulations shows that the inverse Lidov-Kozai resonance is possible for small,moderate and high values of $e_1$. Moreover, such a resonance producesdistinctive features in the evolution of a particle in the ($\Omega_2$, $i_2$)plane. In fact, if $\omega_2$ librates and $\Omega_2$ circulates, the extremesof $i_2$ at $\Omega_2 =$ 90$^{\circ}$ and 270$^{\circ}$ do not reach the samevalue, while if $\omega_2$ and $\Omega_2$ librate, the evolutionary trajectoryof the particle in the ($\Omega_2$, $i_2$) plane evidences an asymmetry respectto $i_2 =$ 90$^{\circ}$.

The inverse Lidov-Kozai resonance for an outer test particle due to an eccentric perturber