Logo has an ugly white box around it on my site header

Ask whoever made the logo for the original file first. If there's an SVG or a transparent PNG somewhere, that beats any cleanup. If not, GIMP is free and does this well: Layer > Transparency > Add Alpha Channel, then Colors > Color to Alpha and pick white. That one handles the soft edges much better than the magic wand, which is what gives you the jagged look. Export as PNG. Cheap trick if it still looks rough: just give the logo the exact same green background as the header. No transparency needed.