Sclerotherapy works by hardening the treated veins, which then gradually fade as they are absorbed by the body. In some cases, especially when varicose veins are severe, the treated veins may feel firm and string-like under the skin. This can cause a sensation of tightness or stretching. However, this is a normal part of the healing process, and these hardened veins typically soften and disappear within 3 to 6 months.