Clean a mesh basket where leaves collect
A basket is easier to keep clean when wet leaves come out promptly and the mesh has room to dry.

Empty it without forcing the leaves through
After the basket has cooled enough to handle, remove the spent leaves into the appropriate household waste or compost arrangement. Avoid pushing a dense lump through the mesh with a spoon. That can distort a fine basket and leave fragments caught where they are harder to reach. A gentle tap or a soft utensil used without pressure is usually a more practical starting point, provided the maker permits it. Do not strike a delicate rim against the sink. Rinse remaining small pieces away in a way that does not send a large mass of leaves into the plumbing.
Clean the mesh and the joins
Follow the basket's material and care instructions. A stainless steel mesh, plastic frame and silicone handle may not all have the same cleaning limits. Use a suitable soft brush to reach the mesh and the seam around the rim, then rinse thoroughly. Looking through the empty basket toward a light can help you notice areas still holding leaf fragments. It is an inspection, not a reason to poke individual holes with a sharp object. If the basket is dishwasher-safe, position it so it will not be crushed or hide its inside from the wash. A dishwasher label does not mean a tightly packed basket of leaves should go straight into the machine.
Give it a dry place to land
Leave the clean basket where air can reach the inside and outside. Storing it wet inside a closed pot makes it harder to tell whether it has dried and can trap old smells. Wash the little dish or lid used as its drip rest too; that surface receives concentrated tea each time the basket is removed. Check the mesh occasionally for loose wires, tears or a damaged join. A sharp or failing basket should be replaced rather than pressed back into shape indefinitely. If cleaning always feels difficult, consider whether a simpler design with accessible surfaces would suit your routine better. The useful infuser is one you can empty, wash and dry without turning every cup into a lengthy task.