Its like cellulite of the eyes, apparently this symptom is evident in the painting of Mona Lisa (on her upper left eye). Once present, xanthelasma does not usually go away on its own. In fact, lesions can grow larger and more numerous so many opt for the cosmetic option of treatment. Presumably your GP has tested blood cholesterol levels? If the xanthelasma is cosmetically unappealing, and if it does not respond to lipid-lowering therapies, treatments include:
Freezing with liquid nitrogen (cryotherapy)
Surgical excision
Laser treatment
Application of a specially formulated acetic acid solution to dissolve the xanthelasma
Electric needle treatment (electrodesiccation)
All of these treatment options may cause scarring, and they do not keep the xanthelasma for coming back or prevent new lesions from developing.