Don't Mind Me
Without Regard For
expression
Remember how 構う is "to care about"? You can convert it into お構いなく to politely tell someone not to care about you. So this means, don't mind me.
It can also mean without regard for, especially when someone keeps doing something without caring about other people, their surroundings, or unfavorable conditions.
The reading comes from 構う, so if you know that you know this!
すぐ帰りますので、お構いなく。
I'll get going soon so please don't mind me.
うちの家のことは、どうかお構いなく。自分たちでなんとかしますから。
Please don't worry about us. We will take care of it ourselves.
社長がOKと言おうが言うまいが、お構いなく話は進んだ。
The discussion proceeded without any regard to whether the president gave his approval or not.