I don't know. I have about two seconds of that in a Cap fic that I started so long ago it's probably no longer canon, and Tony got super uncomfortable, so in my verse at least, I'm guessing they don't. I can see Tony being sort of jealous that Steve had the respect of his father that he didn't have. I can see Steve wanting to fix, too, though, so maybe one night they might have a heart-to-heart about it. Steve being persistent while Tony works on a gadget of some sort and grunts.