If you just have a small degree of marginal skin ischemia, less then 2 mm or so then this should fall off in a few weeks. If you have full thickness skin loss it can take 6 to 8 weeks to heal.
It typically takes 2 weeks or so for all of the scabs and crusts to come off and for us to take off Steri Strips. We change them before this if needed, but we like to keep them on to protect the scabs. Whenever a scab is pulled off or brushed off before it's ready, it leaves a raw area, and this is the thing that makes scars thicker and wider. The more raw dermis that gets exposed the worse the scar is. That's another reason why meticulous closure and approximation of wound edges at surgery is important. Sometimes, depending upon the type of sutures used to close the wound, there may be some extrusion, or "spitting," of suture material as the body is breaking it down, and this can cause occasional opening of the superficial skin edges weeks after the surgery, with resultant scabs too.