This week's A story involves Ollie, Dig and Roy going to the fictional island nation of Corto Maltese (which first appeared in The Dark Knight Returns and was named in honor of the Hugo Pratt character). The team's main goal is to go find Thea and bring her back to Starling City, which we'll get to later, because there's also a spy/action plot.
Before he leaves for Corto Maltese, Dig's ex-wife and the mother of his daughter, Lyla Michaels, a.k.a. Harbinger, tells him that an A.R.G.U.S. agent has gone dark within the country. Dig has announced his intentions not to go to Corto Maltese, but Harbinger talks him into it so he can find the agent, one Mark Shaw (a.k.a. the third Manhunter). I don't know why she couldn't ask Ollie to do it so Dig could stay at home not risking his life and caring for his daughter, but it gives him a plot, so whatever.
In Corto Maltese, Dig has basically no trouble locating Shaw, which should probably be a sign of something, but Dig lets it slide. After some weak tough-guy stuff, Dig satisfactorily proves he was sent by A.R.G.U.S. using an encrypted message on his phone.
What follows is a pretty rote retelling of the plot of the first Mission: Impossible movie. Shaw tells Dig an arms dealer is going to try to buy a list of undercover A.R.G.U.S. agents' names, along with information about their families. He calls it the "actual" list, but I'm just going to call it the NOC list like Mission: Impossible did.
Shaw recruits Dig to help him recover the NOC list, and then quickly double-crosses him. Somehow that thing in Dig's phone helped Shaw decrypt the NOC list, which he's going to sell to the arms dealer the next day.
After getting some help from Smoak to find out where the sale is happening (basically the same place the double-cross did; I can't see any real difference in the shooting locations), Team Arrow is confronted by some mercenaries Shaw hired while Shaw shows off the NOC list to some guys who work for arms dealer Milo Armitage (the guy who tried to buy the earthquake machine last season).
This scene with the mercenaries is important for a couple reasons:
1. Ollie reveals he made a bow out of the furniture in Team Arrow's hotel room, which is patently hilarious.
2. Ollie tries shooting mercs with a bow for a while, but then he gives up on that and just starts shooting them with a gun. I suspect he's going for non-lethal shots, but still. He's just firing a gun at dudes.
By the end of it, Team Arrow has taken down the mercenaries and Shaw is begging Dig to let him fake his death so he can get out of A.R.G.U.S. He hates working for Amanda Waller because...she asks him to to do things? That's what I got from it.
Dig punches him out and hands him over to A.R.G.U.S., because the list being out would have put his family in danger, much like going on this trip put him in danger.