To get the binaries, backgrounds and palettes, download from one of these two sources:
Located in the "palette exporter" folder. This utility simply convert all backgrounds palettes into Microsoft RIFF palette format that you can import in Gimp. This is however not what you will manually do. Those palette files are later neccesary for the image converter to work. To export all the palettes, simply place a headerless FF3us ROM in the same folder as the exporter and double click on the exporter executable. A folder with your ROM name will be created with all the palettes files inside.
Located in the "image converter" folder. In order for the background image to have the same palette order than the ROM, we need to convert existing BBGs rips from non-8bpp-indexed PNG format to 8bpp indexed 256 format with correct palette order. To do this you need at least one BBG rip named "BG_XX.png" where XX is the BBG FF3us ID in hexadecimal. The second thing need is the BBG palette file named "BG_XX_PAL_YY.bin". YY is the FF3us BBG palette index. This correct filename is generated when exporting palettes (see #1) and palette ID for the BBG is fetched from BBG data. You need one palette file and one BBG PNG rip matching for a single succesfull conversion. You therefore can have the 54 palettes files and 54 BBG rips in the same folder as the converter and launch all images conversions at once by clicking on the converter.
Put you exported Gimp .txt palette file(s) in the "palette importer folder". Your palette file must be named "BG_XX.txt" where XX is the FF3us ID of the BBG you just edited in gimp. You also need your ROM in the same folder as the importer. Click on the importer and it will fetch the correct palette ID for the BBG(s) and import the palette file(s) in the ROM. Quick and simple!