Don't check for Moiré patterns until you're looking at an image file at 1:1 pixel size. Moiré patterns can appear on top of a perfect photo whenever the image is naively downscaled without gamma correction. This also happens within the camera display - any Moiré visible while shooting does not necessarily need to be corrected.

There's nothing wrong with choosing to blur out the grill pattern - the photos probably represent the original display signal more accurately.