That lawnmower can't reach the neat contours on your garden bed, but leaving them alone will ruin your yard's manicured appearance. Trimming the edging on your borders is easily done with a gas-powered or electrical trimmer. Before you trim the edge, mow the rest of your lawn as usual and remove any grass clippings. Get as close to the edge as you can without going into it, leaving 1 to 2 inches of long grass to combat with your trimmer.
Turn on your trimmer and test it to make sure it's in good working order. If you're using an electrical trimmer, plug it in.
Walk over to the border edging with your trimmer. You want to cut enough grass to even out the edges and make them flush with your lawn grass, but not remove so much that the edge looks shorter or shallower. Notice the length of the grass at the edge and plan to remove no more than one-third of it for a good trim job.
Turn on your trimmer. Move the trimmer back and forth over the border. As you do this, the nylon string will cut the grass blades. Be careful to hold the trimmer high enough up so that it only removes one-third of the length of the grass.
Walk back and forth along the border, moving your trimmer so that all grass along the edge gets trimmed. When you've finished an area, inspect it to make sure you haven't left any long patches.
Trim any other parts of the border in this area using the trimmer. If you notice stray grass blades later, snip them with hand clippers.