The RI Death Index identifies him as son of James.
In the 1860 Federal Census, Thomas P. & Mary A. Remington are ages 30 & 26, and are living in Warwick, RI. They are near the household of Johnson B. Colvin, whose wife is Almira (Dyer) (Remington). In the Colvin home are Horace, Andrew, & John Remington, sons of Almira by her first husband, Thomas Russell Remington, second cousin to Thomas P. Remington.
In 1870 Thomas & Mary are still at Warwick, with their eight-year-old son Thomas A. Remington. They are near Betsey Remington, widow of George (s/o Thomas & Almira), and her two children.
In 1880 Thomas & Mary are still living in Warwick, RI. Their son is 15.