Now this is a very ‘underrated’ scene. IMO it’s one of the most important scenes that helped strengthen Oliver&Felicity’s bond.
1- This is basically their first 'make up’ scene.
2- Diggle is there to make sure Felicity won’t reveal Oliver’s secret but Oliver is there only to convince her to come back to the team. Bcoz he already trusts Felicity enough to know she wouldn’t say a word to anyone. This is important you guys! As someone who couldn’t tell his secret to his family, his best friend and even to his so called/past-time love of his life, Oliver puts his whole trust in Felicity Smoak, a girl he met just a few weeks ago!
5- We all know back in season 1 Oliver was not the kind of guy who apologized often or accepted that he’s wrong. But here he is telling her that he made a mistake.
6- While they were listening to the news about The Dodger and Diggle tells them about this new villan, Oliver’s watching Felicity very carefully. And then she goes “Oh this psycho is in town? Too bad he isn’t on your list!!!” BURRNN!
Watching Felicity’s reactions, Oliver understood that Felicity wouldn’t join the team again unless she believed that he was ready to do some good for the city. The great thing is, -thanks to her- Oliver also realized he could do this. He could be more than a guy who’s back to his hometown for revenge.
So he goes “I can make an exception. Why don’t you help us catch him?”
He wants her on his team as a friend and this scene also makes me think that if Felicity were to leave the team for good after they saved Walter, Oliver would have found a way to bring her back. Bcoz even back then, she became an important figure in his life that he’s not willing to give up.