Moths do not bite very much the same that humans can. They could, however, inflict injury to garments and fabrics by gnawing holes inside them. This may be avoided by keeping them correctly in sealed bags or cartons.
While adult moths usually do not bite, their larval (caterpillar) stage does have stinging mouthparts. This is the reason it is critical to apply a repell https://ctxt.io/2/AACQr7GpFw