What exactly is "furry?" Unless you use sandpaper or an electric sanding disc, turtle shells are pretty strong. If for some reason you absolutely had to clean off a turtle shell, I'd think one of those blue Scotch-Brite non-scratch pads meant for dishes and say Dawn dish soap (Dawn is recommended by veterinarians for mammals, even baby mammals like guinea pigs) in a warm water solution, and gently clean the shell. Keep it tilted so head is above everything else so any drips run towards the tail, and avoid excess water. Rinse the soapy solution off afterwards with fresh water. If your water is heavily chlorinated, consider buying a gallon of drinking water at a store and use some of that for the soapy solution too.
Think most here will tell you to just leave it be, but if it has a bunch of fungus or stuff it can't shake off, don't think a quick wipe down will hurt. Be mindful to try and keep the water/soap off the skin and neck, and if it pulls it's head in, not to let water go into the neck hole opening. If soap does get on the face/eyes, tilt head DOWN and rinse it immediately with fresh water.
Turtles will leave the water and can travel a little bit to find a suitable spot to lay eggs (often a front yard if near a lake, or similar). Chances are if a female, she might have done that and now returned.