There’s a death notice for Phillis on this link which gives her age and places the family in Drumskellan townland.
Thomas is listed in Griffiths Valuation in 1858. He had plot 27 which was a 5 acre farm. 2 possible deaths for Thomas. 1871 aged 86, or 1875 aged 74, both registered in Londonderry.
The McCarter were apparently still there in 1901:
By 1911, the widow Mary was on her own there:
John McCarter was born 7.2.1867 at Drumskellan. From that I can see his mother was Mary Hamilton. She married George McCarter on 10.4.1862 and their marriage certificate gives George’s father’s name as Thomas. So a brother to the Robert who emigrated.
Family was evidently Presbyterian. Greenbank Presbyterian has records from 1862 onwards and Knowhead from 1826 (baptisms) and 1846 (marriages). Copies of both church’s records held in PRONI in Belfast.
I noted these probate abstracts on the PRONI wills site, which may be the same family:
Administration of the estate of George M'Carter late of Dramskellan Ture County Donegal Farmer who died 7 February 1902 granted at Londonderry to John M'Carter Farmer.
George died intestate so there’s no will but his probate file should be held in PRONI.
McCarter Mary Elizabeth otherwise Mary Eliza of Ashdene Garden City Londonderry spinster died 22 December 1954 at Drumskellan Ture county Donegal Eire Probate Londonderry 3 March to Henry Ridley McCarter confectioner and Winifred Margaretta Harpur McCarter married woman. Effects £808 3s. 3d.
The will itself is not on-line but you could get a copy from PRONI.