Short answer
No, you don't need to worry. A small amount of turmeric is safe for dogs and is even an ingredient in some joint supplements. Just monitor the dog who ate it for any mild stomach upset, like vomiting or diarrhea. If you see those signs, a call to your regular vet for advice is a good idea.
Turmeric — Food safety facts
Safe to share · Dogs · full breakdown on the linked food page
A small pinch is safe and is used in some joint supplements. Large doses upset the stomach.
The full verdict, portion guidance and serving notes are collected on the Turmeric food facts page.