Depends on whether the particular LCD uses a black masking matrix everywhere but over the pixels. If it does, only the pixels can light up, and a grid pattern around all good pixels is impossible, only pixels misbehaving in vertical and horizontal patterns surrounding apparent good pixels but uniformly across the entire screen.
If the LCD does not use an integral opaque optical mask, with the LC material only loosely controlled in polarization along the drive lines and TFTs something has to be done with the light leaking past the row and column lines. I am postulating that the light leaks are the source of the grid pattern if the polarizers do not do a certain job.
If the row and column lines have a low enough duty cycle compared to the sample and hold function at each pixel, the LC polarization everywhere but the pixel locations will have some average polarization rotational factor everwhere approximately the same, and this can be taken advantage of not by exactly crossed polarizers, but polarizers crossed enough that the residual leaked and rotated light past the row and column lines ends up exactly crossed with the front polarizer, establishing a nice black level everywhere, except in those pixel locations where a sampled and held potential rotates the LC material differently and opens the shutter some. I don't know that your LCD works on this principle, but it might.