for the outside or inside? If this were my project I would probably take a piece of thin board and cover it with the fabric. Does the door have a window in it?
Mounting the panel on the door without causing any damage, and so that the panel stays mounted even when the door is opened and closed will likely be one of the biggest challenges of the project.
What type of material is the door made out of?
I used velcro to adhere fabric to wood. https://www.exquisitelyunremarkable.com/2015/03/creating-charm-with-fabric.html
Have you considered gift wrap?
Just tape it into place.