Two-dimensional anti-scatter grids (2D-ASGs) have been developed to selectively capture scattered photons while preserving image signal in flat-panel cone-beam CT systems (CBCT). However, 2D-ASGs affect the response of detector elements underneath grid-septa, producing grid-line artifacts (GLA), which render traditional gain-and-offset corrections ineffective. GLA in the projection images lead to ring-artifacts in CBCT reconstructions, which undermine the improvements in image quality associated with 2D-ASGs. We propose a novel implementation of an exposuredependent gain-correction and notch-Fourier filtering of the projection data to minimize GLA-related ring-artifacts in CBCT. A pixel-by-pixel gain-factor was calculated by dividing the intensities of a flat-field image (with no-ASG) by the intensities of a flat-field image with added ASG, at different exposure levels. Exposure levels were modified using copper filtration of the x-ray beam at six-different thicknesses (0 to 2.5 mm, 0.5 mm increments). Exposure-dependent gain-factors were stored in a multidimensional array and pixel-by-pixel exposure response was characterized using nonlinear curve-fitting. The exposure-dependent gain-correction was applied to 215 projection images of a 14 cm water phantom using a cobalt-chrome 2D-ASG. Residual faint grid-lines were removed using a customized Fourier-notch filter prior to Parker-weighted FDK reconstruction. Traditional gain-and-offset correction produced severe ring-artifacts (i.e., σ = 833.64 HU) when compared to the exposure-dependent gain correction (i.e., σ = 76.16 HU). Additionally, Fouriernotch filtering improved CT number accuracy by 43 HU. Our results suggest that characterization of the exposuredependent response of GLA-affected pixels can minimize ring-artifacts and improve CT-number accuracy, thus eliminating some of the difficulties of 2D-ASG implementation in CBCT systems.