They’ve never been to Budapest.
There were several missions planned there, over the years, but they were either cancelled or sent somewhere else at the last minute.
It becomes a running joke between them: one of them concocts an intimation of the most bizarre circumstances that occurred on this mysterious ‘Budapest’ mission, and the other pretends to have a completely different recollection of that same event. They bring it up to one another at the strangest times.
It begins to drive Tony Stark absolutely up the fucking wall, because as hard as he searches either of their records, even going in through the back door of SHIELD’s personnel databases, he cannot find even a hint of this referenced mission. He’s sure it must have been huge… mind-blowingly huge. Because otherwise why would they keep talking about it?
He actually begins to keep a small notebook of all the events they talk about, in the hopes it will help him figure out what the fuck happened in Budapest.
Head Canon accepted.