Not a direct solution to the question of how to reduce the font size
of the second-subscript "D" -- which has no solution in TeX anyway, as
the "D" is already at its smallest size -- but of possible use anyway:
By inserting a "negative thinspace" ("\!") command right before the
"D", as in
$\int_{\Gamma_{\!D}}$,
the "D" glyph is moved ever so slighly closer to the "\Gamma" symbol.
From a visual/aesthetic standpoint, this serves to clarify that the
glyph is a subscript of the set \Gamma rather than some separate
entity. Best, Mico