Temple Clothing Program offers instructions re: when garments are no longer useful.
Temple Clothing Program, minutes, October 3, 1975, in Devery Anderson, The Development of LDS Temple Ceremonies (Salt Lake City: Signature Books, 2011), 417
Under no circumstances is the sacred clothing to be given to any organization, including the Deseret Industries. Garments and temple clothing that are freshly laundered and in good condition for wear, but for which an individual no longer has use, may be given to an endowed relative or to a bishop for welfare purposes. When garments are too worn for use, the marks of the priesthood should be cut from the garment and either shredded with the scissors or burned. The fabric of which the garments were made then have no further significance as sacred clothing of the Church, and may be used for other purposes if desired, after rendering it unrecognizable as an article of clothing. The authorized-pattern label in the garment should also be cut off and destroyed, or kept for future reference concerning size and style.