Aside from his arcane studies and lofty intellectual pursuits, Doctor Strange does his fair share of mundane research as well. While he definitely wouldn't have bothered looking into former employees of Stark Industries under normal circumstances, a word from Fury had put Quentin Beck on his radar. A man claiming to be from a different Earth is a person of interest, after all. Even so, the Sorcerer Supreme is a busy man with many responsibilities, and in that capacity, he'd been unavailable during the conflict involving Mysterio.

In conclusion, Beck's face and name are a familiar subject to the displaced sorcerer. Beck's reputation? Not so much. Unverified claims of inter-dimensional travel are as good as rumor.

And currently, there seems to been a bigger issue. He ignores the 'hand' quip with a straight expression, having no reason to believe the comment had been made with prior knowledge of his injury.

"If they're not careful, one might be lead to believe they don't want anyone entering their clubhouse. Unfortunately, I find myself in need of exactly that." He jerks a thumb to indicate the closed door, incredulous. "They are asking for individuals to vouch for one another to enter."