I understand all parish records for Beds are on the IGI, so it is strange that her baptism isnt there.
Virtually all Beds baptisms and marriages
pre 1813 have been extracted onto the IGI. Post 1812 entries not are so well covered.
Perhaps the family was non-conformist, or perhaps she was simply wasn't baptised. Or perhaps she was baptised in Buckinghamshire, which is very close to Leighton Buzzard.
But Leighton Buzzard baptisms for this period are on the IGI and there are no baptisms at all of children of George and Mary. When did she emigrate? Have you found her in the 1841 census?
There's no burial of a Mary Green in Leighton Buzzard in 1837. There is however a Mary Green aged 24 buried at Potsgrove, a couple of miles from LB, on 14 Feb 1837. You'd need to check the parish register to see if she's described as the wife of George. The IGI has a marriage of George Green and Mary Evans on 11 Oct 1831 at Milton Bryant, a mile from Potsgrove.
Where are George and Mary's birthdates from?