I'm no expert on this but here's my take. Car mirrors are different that any other mirrors. They're two mirrors in one. You flip it to the night position and the reflections of car lights behind you are greatly dimmed. So there's something about the glass or the mirror backing or something in a car mirror that is responsible for this effect. Maybe that characteristic has something to do with you seeing your lace in the car mirror but nowhere else.
Regards,
John