Perhaps Tony, knowing Peter's character, is somewhat expecting the interruption. He might have a wry smile on his face and then listen to what Peter has to say. He could also play it cool and make a joke about Peter's eagerness to interrupt his meeting, while still giving Peter a chance to explain his reasons.
Peter is likely to be in awe. He might be a bit nervous at first, but also extremely excited. He has looked up to the Avengers for a long time, so meeting them would be like a dream come true. He would probably be stuttering a bit as he tries to introduce himself and show his respect.
Maybe Peter has some urgent news to share. For example, he might have discovered a new threat to the city or a problem related to one of their projects. He could also be in trouble himself and needs Tony's immediate help.
Peter may try to get Tony's attention back. He could show off his own skills or achievements in an attempt to remind Tony of his value. For example, he might go on a solo mission and do an amazing job, hoping that Tony will notice him again.
Peter might barge into the meeting room, his face flushed with excitement or urgency. Maybe he has some crucial information that couldn't wait. He starts talking rapidly, ignoring the initial shocked stares from the attendees. The meeting leader tries to regain control but Peter's words are like a flood, pouring out important details about a project that could change the course of the company's plans.
Peter might be initially shocked and a bit scared. After all, Tony is like a mentor to him. But then he could become defensive, trying to explain his actions or point of view.
He might be in shock at first. Sly has been on his own for so long that seeing his parents could be overwhelming. He could just stand there, speechless, trying to take in the fact that they are real and in front of him.
Tony could be initially shocked. He might not understand why Peter would run away, especially if they had a good relationship before. He'd probably start searching for Peter right away, using all his resources.
Peter might be initially suspicious. After all, in his world, strange things often mean trouble. But then he could also be curious to find out more about this doppelganger. He might try to test the doppelganger's abilities, like seeing if they have the same spider - sense. If the doppelganger seems friendly, Peter could start to form a bond with them, sharing stories about their lives and learning from each other.
Peter might be embarrassed at first. He's been idolizing Spider - Man and now Tony, a real - life hero - like figure, knows about it. But then he realizes that Tony could be an even greater source of knowledge and support, so he becomes more open about his love for Spider - Man.
Peter would probably be really confused at first. He looks up to Tony, and suddenly being kidnapped by him would be a huge shock. He might try to talk to Tony, asking him why he's doing this.