Richard Steevens died in 1710, leaving a considerable fortune which produced an income of £606 (about £100,000 as of 2025) per year to Griselda.

[2][3] Richard directed that upon his sister's death the funds should be used in building, and subsequently maintaining, a hospital in Dublin 'for maintaining and curing from time to time such sick and wounded persons whose distempers and wounds are curable'.

[2] Reserving only £120 per year for her own use, she surrendered the remainder to trustees to build the new hospital.

By 1723 a sufficient portion of the new Dr Steevens' Hospital was completed to accommodate 40 patients, in addition to Griselda's apartments.

Jonathan Swift was one of its earliest governors, and his friend Stella (Esther Johnson) in her will bequeathed £1,000 towards the maintenance of a chaplain.