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Alright, guys, I need to make this clear Tony does not anything about the arrowverse. It was not a thing in his home Universe he knows Oliver queen is the green arrow because of comics but the green arrow was really different in comics than in the show.

He doesn't know-how Oliver became the green arrow because he wasn't that big of hero. The reason that he wanted help Thea but after the first to years 2 he found out Oliver was alive. Oliver didn't want to come home at that time and Tony promise him that he wouldn't tell anyone that he was alive. So he distanced himself from his mom and Thea because he felt like he was lying to them.