This "Before image" was scanned from a Micron advertisement in PC Magazine, and it shows the problem scanning any photograph in any printed material on any scanner. E3 at 50 dpi with all Reset Defaults.
(image © 1996 Sinclair Studio)
Such screened prints are simply poor for use as a master copy of an image.
The appearance can vary, the pattern can be large or small, spots or checkerboard or crosshatching, very dominant or fairly mild. Higher resolutions may not show such a noticeable pattern, but the image will usually at least be degraded, and murky overall.
Be certain to judge your own scanned images when viewed on the monitor at Full Actual 1:1 image size, because the monitor screen dots affect it too. The monitor screen can be a principal part of the interference. Often it looks worse when shown reduced in size on the video.
This is the same scan, all defaults, except that ScanWizard's Descreen filter was enabled, and set to match at "Magazine" level. The filter slows the scan time, and is not perfect, but it's a very good answer for a serious problem. You will find the scanners Descreen filter to be better (easier and more effective) than most other techniques.
Do NOT use the Descreen filter when scanning real photographs. Also it is NOT used for regular printed TEXT. It is used only for images in printed matter.
Traditional procedures to eliminate moiré patterns often include scanning at 2X or more the desired resolution, apply a blur or despeckle filter, resample to half size to get the desired final size, then use a sharpening filter. Ugh! But the Descreen filter does something very similar, it is just much easier to use.
See Kirk'sFFT of the above images.