Can't you just throw it out? [LINK]
Instructions on the proper disposal of "Woodsy Owl" costumes, maintained by the National Symbols Program, an agency of the U.S. Forest Service:
Incinerate the complete costume with the oversight of an official USDA
Forest Service law enforcement officer.
If you do not have access to an official USDA Forest Service law enforcement representative, arrangements will be made for dealing with your costume by contacting the USDA-FS Washington Office at:
C/o National Symbols Program
P.O. Box 96090
Washington, D. C. 20090-6090
- The entire Woodsy Owl costume including each of the separate pieces is to be destroyed beyond recognition.