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This works best in small areas covered with or affected by the plant. Areas with widespread creeping charlie will take a long time to manually remove, so you might consider sunlight deprivation or chemical treatment in these cases.  It is recommended you wear gloves for protection if you plan to pull the plant out by hand. Gloves can prevent blisters, friction burns, and callouses from forming during manual removal. Creeping charlie is a common skin allergen that can cause itching or a rash from contact. Wearing gloves will prevent you from having an unexpected allergic response while weeding. For plants that are especially thick, you should cut off the leaves and vines to make the roots more accessible. You can do this most easily with a few snips from a pair of pruning shears. Once the protective upper foliage is removed, you'll be able to target the roots in the ground.  Keep bits and pieces of creeping charlie collected together off to the side or put it in a bag for disposal later. Lost bits and pieces can reseed your plot with the plant. You may want to avoid doing this on windy days. The wind might blow a stray leaf or vine somewhere else you don't want the plant growing. It is not recommended you use a hoe to break up the soil or cut through the top layer of the plant. This can spread creeping charlie even further. In loose, loamy soil, you may find that the roots pull free with relatively little effort. However, in some cases, the roots may be very stubborn. Grasp the root by its topmost part and apply firm, steady pressure until the roots pull free.  You may need to use a rooting tool, which is shaped like a long, flat-tipped screwdriver, to assist in removing difficult plants or those with deep-sunk roots. You should investigate the soil following the hand removal of roots. If you leave behind root pieces, the creeping charlie may return. The leaves and vines you have cut from the plants could serve to further seed creeping charlie, so be careful when disposing this plant. Avoid places like open compost piles where the wind might carry seeds or leaves back to your plot.  Using a thin tined rake can help you sift through dirt to find remaining creeping charlie plant debris. Even small pieces can contribute to regrowth. Throwing the creeping charlie away in the garbage should be sufficient, but you could also dispose of trimmings by burning them. Be sure you have a fire permit before burning, if your region requires one. After you've weeded out the creeping, you can help prevent regrowth by adding mulch, like wood chips, over the area the plant was growing. Use a regular cover of 2 - 3 in (5 - 7.6 cm) of your mulch for the best effect. Getting the whole root system and removing every seed-carrying leaf can be a tall order. It's likely you'll miss a few and see the plant return. Every time you see the scalloped leaves of creeping charlie reappear, pull it out. Eventually it should stop coming back. You should see the creeping charlie diminish after each weeding, but it can take up to a year or longer before the plant is fully removed.

Summary:
Identify suitable areas for manual removal. Remove leaves and vine growth. Pull up the roots thoroughly. Dispose all clippings and roots. Add mulch to deter regrowth. Remove the creeping charlie as it regrows.