The form of laser treatment used for varicose veins is called an Endovenous laser ablation. The laser fiber is actually in your vein rather than targeting the veins from the surface. The surface treatments with laser are usually used for very tiny vessels that look like broken capillaries and not for varicose veins.
The endovenous lasers are used to target the source of the varicose veins. When the source is treated, this then leads to the bulging veins reducing in size but it does not get rid of them directly. Other treatments like ultrasound guided sclerotherapy, cyanoacrylate or glue and even a phlebectomy are needed to get rid of the bulging veins.