Clean the scratched area with a cleaning solution. Dab leather cleaner or wood cleaner on a dry cloth and apply it gently. Water may also work for basic cleaning.
Cover claw marks on leather with a felt-tip marker. This is the simplest and cheapest way to hide light marks. Use a similar colored marker and immediately wipe away the excess with a cloth.
Buff out the scratches with a wood or leather polish. Apply a small amount to a dry cloth and rub in a circular motion on the affected area. Repeat if you see improvement. Use light steel wool on wood and gently rub with the grain if the polish is ineffective.
Fill in small indentations in wood with wax or wood filler. Rub some of the solution into the scratch and even it out by running something flat over the spot to take away the excess.
Sand down the wood slightly with sand paper to even out shallow ridges. Restain the sanded area with the same color after evening it out.