Soak the Gore-Tex item overnight in a solution of one part white vinegar and one part water. Vinegar should kill the mold, neutralize any musty smell and lift any stain left from the mold.
Spray any lingering stain with a pre-wash stain-treatment solution; Gore-Tex recommends Shout or Spray 'n Wash brands. Leave the solution to absorb for the time indicated in the manufacturer’s instructions.
Wash the garment in warm water, using a detergent specially formulated for synthetic fabrics. The detergent should not contain fragrances, softeners or brighteners.
Dry the item in a drying machine with warm heat.
Spray the item with a coat of liquid water repellant. Find water repellants for outdoor, synthetic fabrics from suppliers of outdoor gear. The repellant should absorb into the Gore-Tex and restore any water resistance compromised by the mold.