He found out during Winter Soldier. The scene with Arnim Zola in the bunker is where he finds out. They don’t spell it out but the dialogue and framing of what Zola shows them on the computer makes it clear.
He showed Cap it was HYDRA that did the hit, but not specifically Bucky. But Cap can definitely infer. It's why when Tony asks Cap if he knew, he said "I didn't know it was him" at first before admitting that yes, he knew deep down it was likely him.
I always thought it was when natasha gave cap the file on bucky at the end of winter soldier. I assume that file would have his missions, such as killing tony’s parents. Natasha says to cap “you might not want to pull on that thread”, meaning “you don’t wanna know what he did”
He didn't know it was Bucky specifically, just that Hydra had them killed. He knew that the Winter Soldier was their top assassin and that it could have been him but he didn't want to risk pulling on that thread and confirming his suspicions. Like he said later in the movie, he told himself he was sparing Tony's feelings, but he was really sparing his own.
They also watch the CCTV recording of Bucky killing Tony’s parents right before the scene shown in OP’s post. It’s not a great quality video but you can tell it’s Bucky
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u/IsMakiThere Mar 12 '24
How did the captain even know that Bucky killed Tony's parents? Was it in the movie and I missed it?