Grapefruit — Food safety facts
Feed with care · Dogs · full breakdown on the linked food page
Small flesh pieces are safe; the peel, seeds and pith contain oils and compounds that can upset the stomach.
Short answer
Yes, the peel can cause stomach upset. A small piece of peel might just lead to mild vomiting or diarrhea. Remove any remaining peel and offer fresh water. Watch for signs of stomach trouble, and contact your vet if your dog seems unwell.