"Refresh" has no effect on what the servers of the FAA website store. Instead, it merely updates YOUR computer browser, which might still be "stuck" in its previous view of the page where the old arrangements existed. "Refresh" CANNOT delete anything, therefore, it merely makes your view of what you have done up to date.
As for your galleries, you have to rearrange your gallery thumbnails too - separately, under the GALLERY edit button. You did the IMAGES reordering. Now do the GALLERY reordering to get THOSE the way you want too.