Surreptitiously means that Strange was very proud of how sneakily he managed to position himself between Childermass and the door until Childermass gives him a Look and he can't help but roll his eyes slightly instead. Well he tried.

He's not entirely sure what to do in this situation. Of course he's sticking around to see that Childermass actually gets healed in the first place. It wouldn't surprise Strange if the other magician tried to cut and run, especially since he's become all the more grumpy.

So don't mind the nosy magician in the background, watching Childermass and Lambert as the examination of Childermass's nose begins. He still doesn't know what to do but well, he can at least watch. And really, Strange has absolutely no medical background but even he can tell that the bruising looks rather nasty. He's quiet for now but inevitably Strange'll have an inane contribution to add to the conversation sooner or later. He takes a few steps closer towards the two, trying his hardest not to get in the way while still seeing what exactly Lambert's going to do.