Using ReplacePart:
l1 = listF;
l2 = newD;
ReplacePart[l2, Catenate[Position[l2, #] & /@ (Join[#, Reverse /@ #] &@l1)] -> Nothing]
(*{{{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}}}*)