I used a wooden milk spoon to cook some eggs with onion. I then used that spoon (after it cooled down) to scrape off some old (more than 24 hours) cold meat food out of a meaty ceramic dish. Presumably the milky spoon still had some pieces of milky onion on it at the time. Is the meaty ceramic dish still ok to use? Does it need to be Kashered?

The dish is fine- just rinse off any residue.