I rewrote the answer due the new information.
The problem was not some ultra-fine canvas texture interfering with ultra-high resolution displays or the camera, but the very well visible colored lines in the canvas. I have marked with blue some of the problematic lines in your screenshot:
These lines cause no problems with your 1600 pixels high display, but interfere heavily with your customer's screen which is only 800 pixels high.
You have following options:
Let it be (probably actually not an option, because your customer can see it as your mistake)
Low-pass filter the image. That unfortunately makes the canvas plastic-like.
Here a heavy filtering is applied to your heavy-moire screenshot only to show, what kind of plasticity I mean:
I will insert the practical methods for the low-pass filtering to the end of my answer.
If you resample the image to a little different pixel dimensions, the moire pattern can be less noticeble
The website can have a possiblity to show different images for different display resolutions. So the big screen owners can see crisper images, the filtered one is for low-res.
How to low-pass filter:
Photoshop's Smart blur is quite optimal for this purpose. It's made for hiding faint details, but saves strong borders. The gaussian blur would need much more tinkering.
- select the cloth area. This case is easy with the quick selection tool
- goto Filter > Blur > Smart Blur and play with the controls
Another practical method is to use some noise sample based noise reduction plugin or stand-alone program. You can show by making a selection which is the unwanted noise pattern. Camera noise model based programs can be unuseful for this.
My filtering example was done with old Neat Image. It was applied twice. I hadn't it as a plugin, so the model was filtered too. The model was restored by cutting and pasting her onto the filtered image.
Both methods gave virtually the same result.
The third way is to subtract a high-pass filterd version, but it's very tricky, because strong borders must be added back and the lost color must be restored. => 1000% more work, mostly with layers and blending modes. The method allows plenty of control, but it's not practical.