Hmmm.
In the 1841 census (transcription), there are some Edward families in Enumeration District No 3, which includes among other places Barras, Largie, Bracks, Cotbank, Bridgestones, Glebe of Catterline, Locherie, Damside, Temple, Farside, Ferneyflat, Belfield, Purleknowe, Harvieston and Burn of
Mendie. See
https://freecen1.freecen.org.uk/cgi/search.pl - and search for Edward* in Kinneff and Catterline.
So Burn of Mendie is the farm or croft where they lived.
All of these places, except Burn of Mendie, are to be found (with some spelling variations) on the first edition of the six-inch Ordnance Survey Map
https://maps.nls.uk/geo/explore/#zoom=15&lat=56.88626&lon=-2.24191&layers=5&b=1 However Burn of Mendie isn't in the census in 1851, and it isn't listed in the index to the Name Book of Catterline and Kinneff. So either it had vanished or it had had its name changed. There is an Edward family at East Largie, and a widowed James Edward at Burnside of Largie.
Either way, parishioners who died there would have been buried in the parish kirkyard at Catterline, which in the 1830s was the only graveyard in the parish of Catterline as opposed to the combined parish of Kinneff and Catterline.
I've looked at the MI book for Kincardineshire, but there's no mention of James Edward and Jane Paul.
Edit:
GR2's post crossed with mine. Good find!