For this information I am very grateful to Trevor Littleton of the Cumbria FHS:-
The parents of Monkhouse & Thomas Graham were Thomas Graham and Ann Bell. She was the sister of William Bell of Tarraby Farm.
Margaret Graham, sister of Monkhouse & Thomas, married James Maguire, a cattle dealer from Co Antrim. In 1841 their daughter Mary Ann married James Forster, who farmed at Tarraby.
When Mary Ann Forster's mother Margaret Maguire died aged 70 in 1850 ("deeply regretted, and most deservedly respected. She was an affectionate parent and a sincere friend to the poor" according to the notice in the Carlisle Journal) she was living at The Beeches, Tarraby. When Mary Ann Forster writes to her uncle Thomas Graham of repairs to the house, it appears that she is referring to work being done to The Beeches. The builders were apparently still at work when the house was put up for let:
Carlisle Journal, Friday 8th November 1850Mary Ann died only a few years after she wrote to her uncle:
To be LET, and Entered upon immediately , an excellent DWELLING HOUSE &c, situate at TARRABY, the residence of the late Mrs. MAGUIRE; consisting of Parlour, Kitchens, Pantry, and other conveniences with Four good Lodging Rooms, Orchard, and Kitchen Garden – For particulars, apply to Mr. JAS. FOSTER, Tarraby; or Mr. CHAS. ARMSTRONG, Builder, Carlisle.
Rent Moderate.
Tarraby, Nov. 7th 1850.
Carlisle Journal, Friday 17th February 1854
At Tarraby, on the 7th inst., Mary Ann wife of Mr James Foster, aged 43, and the last of the family of the late Mr. James Maguire.I don't know whether Thomas Graham is remembered in any monument or tomb at Great Ayton, but he is certainly commemorated in his native Cumbria. There is a monumental inscription to Thomas Graham of Ayton Hall inside Stanwix church.
2 March 2021: I've just realised that I should have added this information quite some time ago
For more on the Graham family of Knockupworth, see Knockupworth: The story of a family by John Bainbridge (details here)