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Even though sandpaper sounds too rough to use on suede, it actually is a great material if you have a gentle hand. Purchase either fine sandpaper (number 000) or use a nail file that you may have at your house. Use soft back-and-forth motions to sand at the gum. Try to avoid directly sanding the surface of the suede. Brush aside any gum that may come off.  Keep in mind that the sanding method will likely affect the suede. A tiny bit of the material may come off as you're sanding. This method is best left after you have tried other methods. It also may be the best method for items like shoes, which are below eye level. If your suede item is something that people will be looking at up close, keep in mind that the material will be affected. Sanding suede with a brush or emery board can affect the nap, or texture of the suede. After sanding, take a toothbrush, nail brush or suede brush and gently brush the nap of the suede, going in one direction. Brushing the suede can also brush away the gum removed during sanding.

Summary:
Purchase sandpaper or a nail file. Gently move the sandpaper or nail file over the gum remains. Brush with a suede brush.