Any mechanism or item that keeps your robot within starting size limits must be on your robot in the match. As such, you cannot take off the rubber band after getting inspected it with it.
Also, to my knowledge, you cannot have a star or the perimeter keep your robot within starting size limits because I don’t think that you can be inspected with a star holding your robot together.
If I can add on, your robot must be checked to be within the size limits, which the star/object is not allowed to be on the robot at that time. If your robot seems to stay within the size limits without an object, and the robot needed the object to stay within the limits for a competition, then that means that you have made a change after getting resized, which means you have to be resized again, and again without the object.