It's not only the BwB. What about Gendry and Melisandre? So add team Dragonstone. Then there is this Hot Pie baking wolf bread at the crossroad's inn - you think he will keep the secret? Half the realm knows that Arya is travelling the Riverlands. Varys should have found out.
Arya has incredible plot armor. Show Tywin has seemingly forgotten that Ned Stark had two daughters, Cersei never mentions to her father that Arya Stark is missing and that she sent out Baelish to find her; Baelish himself doesn't even tell Sansa that he found her at Harrenhal, following ancient House Stark rule from the books...
(They said it together: "Don't...tell...Sansa!")
The BwB, The Hound and LF know that Arya is alive and well. If Varys really doesn't know, it's time for him to retire!
As they were leading their dragons behind a pair of direwolves over the smoking ashes of the Twins with the charred corpses of Others beyond count, the King turned with a sad face to his dashing young ally from Braavos, only recently chosen for Sealady.
"I will miss you, little cousin, but who knows..."
They said it together.
"...different roads sometimes lead to the same castle."