The Gemara (Hullin 105a) rules that meat stuck between the teeth is still considered meat:
אמר ליה רב אחא בר יוםף לרב חםדא בשר שבין השינים מהו?
קרי עליה "הבשר עודנו בין שיניהם"
(My translation:) Rav Akha said to Rav Hasda, "What is the law of meat stuck between the teeth?" He answered him with a pasuk: "'the meat was still between their teeth (Bamidbar 11:33)'"
Q: מי חשיב בשר שלא לאכול גבינה
עמו עד שיטלנו?
A: אלמא מיקרי בשר
It seems from Rashi that it is assumed in the question that even if meat stuck between the teeth is considered meat, removing it would be enough to permit dairy consumption.
The Ran (last few lines of D"H אמר) specifically writes that removing the meat is enough and that additional waiting is not necessary, but suggests a cleaning of the palate first.