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The term describing a granulated inflammation of the eyelid that may necessitate surgical excision if it persists is chalazion. A chalazion is characterized by a blockage of one of the meibomian glands, leading to a firm lump on the eyelid. While initial treatment may involve conservative measures such as warm compresses or topical medications, persistent cases that do not improve may require surgical intervention to remove the blockage and alleviate symptoms.

The other conditions listed do not fit the definition provided. A stye, for example, is an acute infection of an oil gland at the base of the eyelashes, usually causing pain and swelling but typically resolving without the need for surgery. Blepharitis refers to inflammation of the eyelid margins, often manageable with conservative treatments, and does not specifically denote granulated inflammation suitable for excision. Pterygium, on the other hand, involves growth of tissue on the conjunctiva and usually does not involve the eyelid in the same manner as a chalazion. Thus, the nature and treatment approaches for these conditions distinguish chalazion as the correct term.