We present numerical simulations on the correlated two-electron momentum distributions for the recollisional ($e, 2e$) process in nonsequential double ionization (NSDI) of helium by an 800-nm laser field at an intensity around $4.5\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{0.16em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$, based on the improved quantitative rescattering model, in which the lowering of the kinetic energy required for the electrons to escape from the parent ion due to the presence of electric field at the time of recollision has been taken into account. According to the QRS model, the correlated two-electron momentum distributions for laser-induced ($e, 2e$) collision in NSDI can be factorized as a product of the returning-electron wave packet (RWP) and the field-free differential cross section (DCS) for ionization of the parent ion by the impact of the laser-induced returning electron. The RWPs which describe the momentum distribution of the returning electrons are obtained within the strong-field approximation for high-order above threshold ionization. In the calculations of the DCSs for electron impact ionization of ${\mathrm{He}}^{+}$, the precollision Coulomb interaction between the incident electron and the parent ion and the postcollision Coulomb interaction between the two outgoing electrons are considered. In addition, the dynamic screening (DS) of the three-body Coulomb interactions in the final state, due to the fact that the strength of the interaction of any two particles is affected by the presence of the third one, has also been taken into account. It has been found that while the postcollision Coulomb interaction is responsible for the observed fingerlike structure, the precollision Coulomb interaction changes the orientation of the two fingers from $\mathsf{V}$-type to parallel, the final state DS reduces the separation of the two fingers, and the lowering of threshold energy shifts the two fingers towards smaller momenta. All these effects improve the agreement of the simulated results with the experimental results.