The Church of Ireland building that occupies the site today, dedicated to St. Carthach, sits within a notably circular graveyard in the townland of Gransha Lower, and that circularity is itself a quiet signal of antiquity; circular enclosures are often associated with early medieval ecclesiastical foundations in Ireland, pre-dating the more regular geometries that came later.

By 1871, when the historian and writer Mary Frances Cusack recorded what she found there, the medieval church had already disappeared as a standing structure. She noted that scattered stones of the old building lay about the graveyard, and that one stone nearby was hollowed in the shape of an inverted cone, around which people paid rounds, meaning they performed a traditional circuit of prayer or devotion. This stone was known as Cloch-Mochaeda, or the stone of St. Carthage Mochaeda, connecting the site to an early Irish saint whose name survived in the place-name Cill Tulach, the church on the hill. The architectural fragment recorded at this location is one of two surviving remnants associated with the medieval church site, the second being Cloghmacudda, situated approximately 123 metres to the east. The field immediately to the south-west of the graveyard was already labelled Church Field on the Ordnance Survey six-inch map of 1841, suggesting the local memory of the site's sacred character was firmly in place even as the physical remains dwindled.

The graveyard is accessible from the public road to the south, with a second entrance at the north-east that once oriented visitors towards Kiltallagh House, 137 metres away. The stones themselves are easy to overlook, distributed without fanfare among the headstones, but the hollowed cone-shaped stone described by Cusack represents the kind of devotional object that in Irish tradition often outlasted the formal religious structures built around it.