This paper deals with the solution bounds for discrete-time Networked Control Systems (NCSs) via delay-dependent Lyapunov-Krasovskii methods. Solution bounds are widely used for systems with input saturation caused by actuator saturation or by the quantizers with saturation. A time-delay approach was introduced recently for continuous-time NCS under a weighted Try-Once-Discard (TOD) protocol in , where actuator saturation was not taken into account. In the present paper, we develop the time-delay approach for linear (probably, uncertain) discrete-time NCS under the weighted TOD protocol in the presence of actuator saturation. A novel Lyapunov-based method is presented for finding the domain of attraction. Polytopic uncertainties in the system model can be easily included in our analysis. The efficiency of the time-delay approach is illustrated on the example of a cart-pendulum system.