The presentation of a reddish, granulomatous tissue mass protruding from a deep carious lesion in a young patient is characteristic of a pulp polyp (chronic hyperplastic pulpitis). This occurs when the inflamed pulp tissue proliferates and extrudes through an open pulp chamber, especially in teeth with open apices and rich blood supply, common in children. Unlike abscesses or cysts, a pulp polyp is a vital, hyperplastic response of pulp tissue rather than necrosis or cystic degeneration. The lesion is usually painless and appears as a granulomatous growth that bleeds easily on probing. Management often involves removal of the affected pulp and restoration of the tooth.

Reference: Shafer's Textbook of Oral Pathology, 7th Edition.