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Follow the advice from the Master Strop Artisan. Neil Miller

http://straightrazorpalace.com/strops/74435-curling-strop.html

Try using the middle hinge on the door. Also stand and center yourself between the strop. See if standing and stropping helps eliminate the curling problem.

Push the middle hinge pin up a 1/4 of an inch on the bathroom door. You can hang several strops in this fashion using a key ring.

Do you have one end of the strop attached to a solid unmovable surface, (for example middle hinge on your bathroom door). Pulling the strop taunt should remove the curl. Can you post a picture of...