A granulated inflammation of the eyelid that may be removed surgically if it does not subside is a:

A chalazion is characterized by a granulomatous inflammation of the eyelid, typically resulting from a blocked meibomian gland. This blockage leads to the accumulation of secretions and can cause a firm, painless lump on the eyelid. When a chalazion does not resolve on its own through conservative measures, surgical intervention may be required to remove it. This distinguishes it from other conditions that may present on the eyelid.

In contrast, conditions like a stye (or Hordeolum) are usually acute and painful infections of the glands, while pterygium involves a growth of tissue on the conjunctiva that may encroach upon the cornea, often associated with UV exposure. Xanthelasma consists of yellowish cholesterol deposits near the eyelids and is not associated with surgical removal for resolution. Thus, the unique nature of a chalazion, particularly its potential for surgical treatment if persistent, is what makes it the correct answer in this context.