Assuming of course that this is true then I would have called the go around. When we were nicely stabilised in the climb out (or level off potentially depending on the MA altitude given that they were at 3700ft allegedly) I would then reach for the PA handset and pass it to the checker and ask them ever so nicely if they could let the passengers know what is going on and the reasons for us going around. We would then enter a hold, sort ourselves out and brief for the next approach. The rest can get discussed on the ground when the parking brake is set.