Using ReplacePartDelete
and Position
to delete cases from newD:
l1 = listF;
l2 = newD;
ReplacePart[l2
Delete[l2, Catenate[Position[l2Position[l2, #] &Alternatives /@@@ (Join[#, Reverse /@ #] &@l1)] -> Nothing]&@l1]]
(*{{{7, 9}, {9, 2}}, {{6, 7}}, {{6, 7}}, {{2, 11}}, {{7, 8}}, {{11, 1}}, {{1, 5}, {5, 7}},
{{7, 8}}, {{11, 1}}, {{8, 6}}, {{2, 11}}, {{8, 6}}}*)