Not sure if this would help, but perhaps suggest to your care agency that the carer wear aprons? The company has a duty of care to you and their own staff to provide PPE for health and hygiene reasons. Our carers wear their own clothes, but wear gloves when handling my husband for this reason. It is the same as in a hospital and in food preparation - so why not in your home when they are providing a service?

This perhaps is not addressing the root cause of this issue which appears to be the carer himself, but may be a happy medium until something else is sorted?