We have studied the quantum confinement, applied hydrostatic pressure, and temperature dependence of the binding energy of a magnetoexciton bound to a ionized-donor impurity in GaAs/Ga1-xAlxAs quantum wells, taking into account the spin-orbit coupling between the (Γ7v,Γ8v) and (Γ7c,Γ8c) multiplets, including the Al concentration, temperature, and applied hydrostatic pressure dependence on the electron effective-mass me(P,T,x) and the Landé ge(P,T,x) factor by using the well known five-level k · p theory. We have found that the binding energy Eb increases with the strong geometrical confinement, as well as with the growth-direction applied magnetic field. The presence of the ionized-donor impurity clearly increases the heavy-hole exciton binding energy. The quantum confinement, in part determined by the height of the barrier potential-well, i.e., by the Al concentration and the hydrostatic pressure, contributes to enhance the binding energy. Also, we found that the exciton binding energy increases with temperature due to the different temperature band-gap dependence of the well and barrier regions, which conduces to a net increasing of the potential barrier. Also, we have obtained a good agreement with previous theoretical and experimental findings. We hope the present work must be taken into account for the understanding of experimental reports and for the design of optoelectronic devices with multiple technological purposes.