How could I remove the broken capillaries on eyelid? (photo)

Those are normal blood vessels.  I do not recommend messing with them.  No one notices those but you.  Your eyelids need those vessels.  If a goofball tried to laser them close, there is a risk that the eye could be harmed. Just forget about it. 

Electrosurgery with a Hyfrecator at low wattage may be helpful for eliminating the appearance of the small vessels on your eyelids. Consider consulting with a reputable cosmetic dermatologist for evaluation. Thank you. Dr Joseph

Laser treatment would help these venules, but carries significant risk and probably is not worth it.