Extending my method from Cleaning of scanned photo overlaid with pattern (see post #2), this is my method to remove the pattern. I might eventually write a filter or a more official tutorial for it. List of steps (wow, it took me such a long time to write this; props to all tutorial writers!):
A. Original image.
B. Split details (wavelets). The important thing is to make it so that only the last detail scale has the offending pattern. Crop:
C. Fourier transform (fftpolar) of this last detail scale. We are interested in editing the spectrum. Normalized for web viewing:
As you can see, the contrast is quite low. To make it easier to edit in GIMP 2.9.x, we could change the gamma and normalize to 0-1. Just remember to reverse this transformation! Normalized for web viewing:
D. GIMP 2.9.x. Now use the clone tool to remove the 4 lines that extend to the edge of the spectrum. Where the lines touch the edges, there are also small noise clouds. Remove them too.
Why is it lighter? If you recall, you need to reverse the previous gamma and range correction!
E. Finally, you need to reinsert this spectrum back into the workflow. Replace the old one with this new spectrum and then reverse all of your steps.
a) Reverse the Fourier transform.
b) Reverse the split details procedure. For some reason, this new detail scale is too strong now, so one thing you need to do is shrink its influence. For the mountain image, reducing its range to 75% is ideal.
Without reduction:
Good copy:
