All but last d are sharpened, but even if last were, the tune would not be one of the 7 normal 'Greek' modes. I have not found the tune elsewhere under any title. 'Theme code' is 51H2H4 11H2H5.

X:1
T:The Unfortunate Rake
N:from Crosby's 'Irish Musical Repository', 1808
N:(for The Wandering Harper, not Unfortunate Rake)
L:1/8
M:6/8
K:Em
B|B e e e f g|f ^d B A G F|E e e e f g|f ^d BB2 A|\
B e e e f g|f ^d B A G F|G B e G3/2 A/ B|A G F E2||F|\
G B B B3/2 A/ G|F ^D F A3/2 G/ F| G B E G3/2 A/ B|\
A G F E2F|G B B B3/2 A/ G|F ^D F A3/2 A/ g|f3/2 e/ ^d e =d B|\
A3/2 G/ F E2|]