Scan the photo in a fairly high resolution - at least 1200dpi for a print, 4800dpi for a negative. Scan so you get an image that’s (say) 5 or 6 times bigger on a side than you need.
Use image/encoding (or image/precision, depending on gimp version) to choose 16 bits per pixel non-linear (alpha) mode.
Use filters/blur/gaussian blur to remove the background pattern - try a radius of 11 pixels and see what happens.
use image->scale image, and try appending /6 to the width in pixels in the text box and pressing tab, then enter, to make the image one sixth of its size on each side
Use filters/enhance/sharpem (unsharp mask) to bring back the details lost in the blur.
But i am guessing about the nature of the pattern here.