The best way to dispose of used black fiberglass tissues is to place them in a sealed plastic bag to prevent the release of fibers into the environment. Avoid flushing them down the toilet as this can cause plumbing issues and environmental harm. Instead, dispose of the bag in a regular trash can. If the tissues are contaminated with hazardous substances, follow local guidelines for hazardous waste disposal. Always wear gloves and a mask when handling fiberglass tissues to protect yourself from inhaling fibers or skin contact.