You can search for Moiré on the search engines and you willfind a few techniques to remove it, of variable effectiveness. TheDescreen filter in the TWAIN driver is usually one of the best methods.Not all scanners provide this. Microtek and Umax provide excellentdescreen filters.
Traditional procedures to eliminate moiré patterns without theDescreen filter often include scanning at 2X or more the desiredresolution, apply a blur or despeckle filter, resample to half size toget the desired final size, then use a sharpening filter. Ugh! The Descreen filter does something very similar, and is easier to use, but manual methods offer more control.
Higher resolution is better able to fully resolve the screen dots without moire, so do that first, and then resample smaller to final desired size. I often say here to scan at 2X desired resolution for descreen, but that really means to scan AT LEAST AT 300 dpi. If 600 dpi is practical (meaning, if your system can survive that effort), then 600 dpi will be better. Smaller page areas may be practical at 600 dpi, but a full page color image will be 100 MB. Regardless if 300 or 600 dpi is used, then resample the image to smaller final desired size. Then sharpen with USM (last). A VERY MILD blurring before the smaller resample can help too.
Samples of alternate methods:

The first image above was scanned at 300 dpi without the Descreenfilter. Then the Photoshop NoiseDespeckle filter was used, andthen it was resampled to half size and then sharpened with USM. Thispattern exists as part of the image, and the only way to get rid of it isto blur it out of existence. Resampling to half size is a blurringoperation in itself, and is important to this descreen process. ThenUnsharp Mask sharpening helpsrestore sharpness.
The second image above was scanned at 300 dpi without the Descreenfilter. Then the PhotoshopGaussian Blur filter was used, and thenit was resampled to half size and then sharpened with USM. The finalimage is not as sharp as with other techniques, but this is a variable,the Gaussian Blur and the Unsharp Mask both have parameters. Gaussianblur has a Radius parameter, and best results are with that set the sameas will be used in the Unsharp Mask parameter.
TheMedian filter is very similar, it smooths differences inpixels. Some Median filters also have a Radius parameter. Results lookthe same, I won't repeat it here for web page speed concerns.
Only use one of these filters, not all three.
These filters were in Adobe Photoshop. PhotoDeluxe has the Despecklefilter that works well, and a Gaussian Blur filter that is named Soften.
Paint Shop Pro 5.0 has the Despeckle, Gaussian blur, and Medianfilters that all work well.
PhotoImpact has Despeckle, Gaussian blur and Moire filters.
My own opinion of the best general technique is to scan large (atleast 300 dpi) using the Descreen filter, then to resample to the smallerdesired size. Then sharpen with the Unsharp Mask filter. The large photoon the first Moiré page (two pages back) was done this way.
Scanning at high resolution with the Descreen filter and thenresampling smaller is effective to remove moiré, but it willdefinitely consume vast amounts of memory, and so may not even bepossible on many computers. Instead of 300 dpi, scanning at "only" 2Xresolution with the Descreen, and then resizing to half size would reallydo the same thing.
Frankly, the Descreen filter at 300 dpi is a struggle, but memory ismighty cheap now! The Descreen filter slows the scan time, and is notperfect, but it's a very good answer for a serious problem. You will findthe scanner's Descreen filter to be better (easier and more effective)than most other techniques.
In the 300 dpi scan, even without the Descreen filter, themoiré is much less visible than in the smaller image, but is stilldetectable. With the filter, it's rather good, but not perfect.Downsampling by half then helps considerably, but the image will needresharpening. Resampling helps because it is a blurring process, itaverages and blends the colors from multiple pixels to create oneresulting pixel. Detail is lost, including the moiré detail too.And after the resample, sharpening with a Unsharp Mask filter isespecially needed. You do not want to sharpen until after the pattern isremoved, that would aggravate the problem. Scanning at 2X and resamplingsmaller is not the usual scanning procedure, but moiré is a verytough problem.
Again, realize that you must judge the image on the monitor only whenviewed at Full Actual size. A reduced size video view often appears worsethan it is. The monitor's internal physical dot grid can aggravate it andmake it look very different. Therefore, it is possible that in somecases, the pattern may not be as noticeable when printed.
Other methods:
Since resampling is a blurring operation, and blur is what we want forremoving moiré, some say to resample back down in two steps,halfway first, then to the desired size. I do not find it necessary to doit this way, but it's another idea.
It is said it helps to scan at exactly double the screen filterfrequency, that is, 133 lpi for most magazines X 2 = 266 dpi, and 85 lpifor newspapers x 2 = 170 dpi. I don't find that this helps. Thescanner CCD cells are 300 dpi or 600 dpi, regardless if you tell it toresample to 266 dpi or not. However, severity does vary with resolutionand resampling. That is, increasing resolution from 100 dpi up to 266surely does help, but decreasing from 300 to 266 dpi probably does not.
It is also said it helps to rotate the original slightly on thescanner bed. This is viable for Black & White images, but I don'tfind it helps color much, although it can change the appearance. Thecolor screens are sophisticated beyond belief, and contain multiplescreen angles within them. There are four screens, one for each CMYKcolor. Typically the screen for each color is rotated 30 degrees from theothers. The prepress people creating this screen have substantialproblems of their own with moire in the screen itself. Computers are usedto introduce random alteration of the pattern. The subject is reallyquite complex and all images are different. Our rotation of the originaljust introduces yet another problem, and there is no one angle that willsolve anything. Straightening a rotated image is simply resampling, pureand simple, from one grid to another. In my opinion, themoiré reduction benefits come from the blurring of the resampling,and not from the rotation.
Concerning general rules, images vary, screens vary, patterns vary,and anything you do will change something. To form a general rule, youneed to be able to duplicate the results in a general way.
You can see similar moiré patterns if you lay two pieces ofwire window screening on each other, rotate one at an angle from theother, and look through the two of them at a light. In some cases, yousee moiré on video screens, and monitors sometimes have amoiré reduction control. You have seen this effect on TV when theweatherman forgets and wears his pinstripe shirt or herringbone jacket.It is optical physics. It is not the scanner's fault, I think it's IsaacNewton's fault! 😊