The McGinnis family tree on Ancestry has John Grue & Mary Doherty with their daughter Mary born in 1875 in Co. Tyrone. It has Mary junior marrying John McCormick and moving to Motherwell where their children were born 1896 onwards. No date or place of marriage. Parents both died around 1900. There’s no sources on it, so it looks like the information is speculative. You might want to contact the tree owner though to see if they can add anything.
My view is the Mary & John who married in Loughgall in 1895 are the couple who went to Motherwell, and that for some unknown reason, Mary changed her parents names when she re-married in 1915. The informant for her death probably copied the information from her marriage certificate, so I don’t give it the same weight. Mistakes on death certificates are common because the informant often never knew the deceased’s parents. There was only the 1 McCormick – Grew marriage in Loughgall in 1895. The couple in Scotland have to be that same couple really. Where else would they have got the date and place of the marriage from?
This looks to be the family that goes with the 1895 marriage certificate, in the 1901 census:
Same family in 1911. They have bumped their ages up a bit since 1901. (That was to do with eligibility for the old age pension. Lots of people did that in Ireland in 1911). Married 45 years, 11 children of whom 7 were still alive.
Their daughter Mary was born 31st March 1869:
There’s no sign of John McCormick and Mary in the 1901 Irish census which fits with them having left Ireland.
The 1915 2nd marriage shows that Mary said her father was dead and her mother alive at that date. Peter Grew from Keenaghan died in 1911, so that ties in. His wife was still alive then.
Catherine Grew died in 1918, so that ties in too. Interestingly the informant was her son Joseph Grew “who caused the body to be buried. 40 Graham St, Addiewell, Scotland.”
Joseph was born in 1875:
Probate abstract from the PRONI wills site:
Administration of the Estate of the late Peter Grew Senior, Keenaghan, Co. Fermanagh, Farmer, who died 7 August 1911, granted at Armagh 20 December 1919 to Peter Grew Junior, Labourer, the son. Effects: £68 7s 6d.