Within the framework of the improved quantitative rescattering (QRS) model, we simulate the correlated two-electron momentum distributions (CMDs) for nonsequential double ionization (NSDI) of Ar by elliptically polarized laser pulses with a wavelength of 788 nm at an intensity of 0.7 × 1014 W/cm2 for the ellipticities ranging from 0 to 0.3. Only the CMDs for recollision excitation with subsequent ionization (RESI) are calculated and the contribution from recollision direct ionization is neglected. According to the QRS model, the CMD for RESI can be factorized as a product of the parallel momentum distribution (PMD) for the first released electron after recollision and the PMD for the second electron ionized from an excited state of the parent ion. The PMD for the first electron is obtained from the laser-free differential cross sections for electron impact excitation of Ar+ calculated using state-of-the-art many-electron R-matrix theory while that for the second electron is evaluated by solving the time-dependent Schrödinger equation. The results show that the CMDs for all the ellipticities considered here exhibit distinct anticorrelated back-to-back emission of the electrons along the major polarization direction, and the anticorrelation is more pronounced with increasing ellipticity. It is found that anticorrelation is attributed to the pattern of the PMD for the second electron ionized from the excited state that, in turn, is caused by the delayed recollision time with respect to the instant of the external field crossing. Our work shows that both the ionization potential of the excited parent ion and the laser intensity play important roles in the process.