The part was easy to order and relatively inexpensive. The ice dispenser chute cover / flap sits inside the door and creates a thermal barrier/seal between the internal ice box and dispenser and the exterior of the ice / water dispensing area. When the flap does not seal the chute the dispenser will ice up and not work; that's how I found out my flap was broken.
The common issue seems to be that the flap is held closed by a spring that is mounted on a plastic "axle" that is part of the flap's structure. The plastic is not very strong, the axle is relatively thin and not reinforced, and is always under load. So, it can break and the replacement part is not built any differently or from different materials than the original. Unfortunately, I think the design is prone to breaking and expect this to happen again.
The several procedural write-ups provide good guidance on what you need to do to access and replace the seal. The one thing I would highlight is that the short, straight leg on the spring that lies flat on the top soft part of the flap when it is not installed, MUST be secured in the cut-out groove that is located just above where the flap sits in the carrier. The flap will not work otherwise. The groove comes to an arrow-like point towards the flap and that's where the spring leg will sit. Get the spring fitted first before you work on seating the short axles on the sides of the flap.
As mentioned elsewhere, you need to seat the long arm on the flap inside the white "cup" in the cover housing. I would install this side first after seating the spring. The arm sits in the large open area of the cup, which rotates when there is a call for ice. The smaller diameter ridge inside the cup will manipulate the arm to rotate the flap open, after which the cup will rotate again, release the arm and the spring will hold the flap closed. After you seat the long arm side, you may find that the other side is more easily seated if you slide the the short axle slightly below its seating location and then gently pry and work it upwards into the seat.
Take your time and good luck.