Hi Lee and Bobaffinity,
thanks for trying to help.
I was in a hurry and solved the problem by myself — but it was very hard work.
1. I selected the piece of clothing affected and added a new layer in colour mode
2. I removed the rainbow colours by painting them over with brush in color—mode
on this layer.
3. With the selection on the background layer I made a new layer in colour mode and filled it with white.
4. Above the background layer added a hue\saturation layer to remove the remaining structure / pattern of the moiré by adjusting colour
Since this last step only removed some parts of the pattern (as there were different patterns on the whole piece) I ended up stamping the thin lines or replacing them line by line, still trying to keep the texture of the cloth.
Lots of hours of work!
I did this in Photoshop, unfortunately.
I like Affinity but am not much used to it by now, so Photoshop worked quicker for me.
One thing that still keeps me from switching completely to Affinity is that (as far as I know) EXIF and especially IPTC is not supported completely.
Tom