Can a very small broken capillary on upper eyelid be treated with laser?

Short Wave Diathermy, or the use of a very lightly applied electric current to the skin, unlike lasers and light therapies, has a many decades' long track record for both safety and efficacy for treating capillaary telangiectasias ("broken blood vessels") on the face, particularly on the cheeks and nose and elsewhere. The tip of a very thin probe is placed on the surface of the skin directly over the troublesome capillary and the light current generated does the rest. I typically give my patients a mirror, so that they can watch as the broken blood vessels "magically" disappear right before their eyes. You would be wise to consult with an experienced, board certified cosmetic dermatologist who can provide this surface and be quite wary when being hawked this or that expensive laser or light-based device, since many of these here-today-gone-tomorrow devices have not stood the same test of time. Hope this helps and best of luck.