Killinkere is the name of both a Catholic and Church of Ireland parish, located about 10km to the south west of the town of Bailiborough. There's a large gap in Catholic records for the parish between 1790 and the 1840, but Church of Ireland records survive for this timeframe and RootsIreland pay-website have transcript which include the marriage you mention - but still no sign of a baptism for Thomas in this parish... Bailiborough Church of Ireland records are only available back to 1824, the earlier volumes are listed as lost
The marriage took place in Killenkere Church of Ireland on the 24th August, the groom's residence is recorded as 'Monaghamore, Bailieborrow', the bride's residence as Envigaroge, which I suspect may be a mistranscription or variation for the townland of Invyarroge which is in the parish of Killinekere. Marriages generally took place in the bride's parish. George's residence of Monaghamore seems to be a mistranscription also, maybe the original record is hard to read - closest match I can see is Monaghanoose which is in Bailieborough civil parish.. a check of the later 1856 Primary Valuation Record (Griffith's) for the townland show a James Greer holding property in this townland, so looks promising..
RootsIreland also has a number of other Kellet marriages in Killinkere Church of Ireland parish which might be worth checking out as they could be related, including at least one with the same residence of 'Envigaroge' as your Elinor, e.g. a Simon Kellet married Mary Stafford on the 4th May 1803, her residence is given as Cornedan, which is probably a reference to the townland of Corraneden in the same parish.
There seems to be a second George Greer with wife named Ellen in the area at around that time as there are Church of Ireland baptisms for parents with these names in Bailieborough just after your Greer family left for Canada (Church of Ireland baptism dont generally include mother's maiden surname so can be difficult to search).
p.s. I see Thomas on the 1861 census at the location you mentioned, age 38, born in Ireland religion 'Episcopalian' which is Anglican, so Church of Ireland here.