Searching for an unordered triple in a list of triples

This seems to be a case for OrderlessPatternSequence

tT = {{7, 1, 2}, {7, 2, 3}, {7, 3, 8}, {7, 1, 6}};

MemberQ[tT, {OrderlessPatternSequence[1, 2, 7]}]

True

Or define a function to wrap the second argument of MemberQ:

foo = {OrderlessPatternSequence @@ ##}&;

MemberQ[tT, foo @ {1,2,7}]

True

MemberQ[tT, foo @ #] & /@ {{1, 2, 7}, {3, 8, 7},{1, 2, 3}}

{True,True,False}

If the order will never matter for your lists, you can use an Orderless head rather than list.

I use slist (sorted list) :

ClearAll[slist]    
SetAttributes[slist, Orderless]

Then Mathematica will automatically sort any input given to slist :

slistT = slist @@@ T

{slist[1, 2, 7], slist[2, 3, 7], slist[3, 7, 8], slist[1, 6, 7]}

This is the way Mathematica handles functions like Plus or Times which don't care about the order of their elements.

In your case, you can do

 MemberQ[slistT, slist[7, 1, 2] ]  (* True *)
 MemberQ[slistT, slist[7, 2, 1] ]  (* True *)

Another workaround

Xor @@ Sequence[MemberQ[T, #] & /@ Permutations[{7, 2, 1}]]

(*    True    *)