Take the Lieutenant's Insignia to Neeru Fireblade and speak to him. Gauge if he believes you are a member of the Burning Blade and then return to Thrall in Orgrimmar.
Now let us see if this insignia you found is worth the effort.
There is a warlock within the city who believes he has my trust. He does not know that I realize where his true loyalties lie. He is in fact the leader of the Burning Blade. But do not rush off to do battle with him; he has a purpose, and we shall use him against our enemies.
Take this insignia to him in the Cleft of Shadow here in Orgrimmar, speak to him and see if he believes you are one of his own, then return to me here.
Excellent! Most excellent, <class>!
What you have done this day is only the first step in a much broader foundation--a foundation that we will build the destruction of the Shadow Council on, once and for all.
Tell me all he said... and leave not one word out--it may be more important than you realize.