Make her open her mouth and look inside before she leaves the table. This is bad for her teeth.
Milk rot is where a child has a bottle in their mouth all night, the milk continuously drips onto the teeth and the saliva does not get to do it's job of rinsing the mouth. If a person drinks milk and swallows it their teeth don't rot from it, it's the constant supply of milk that rots the teeth.
This is the same concept, the food in her mouth is prohibiting the saliva to rinse her teeth off after eating. The food is sitting there eroding her enamel and basically decomposing (part of the digestive system) so she does have an urgent need to get this out of her mouth.
It sounds like this is a battle in the making. If you want to protect her teeth, keep her from possibly choking to death from this food not going down right while she's in another room, etc....then you have to take a stand and make it an issue/battle/war. This is not a simple "I'm not going to mind you" thing. This is a health issue that she cannot do. It's that simple. Make her open her mouth and show you inside her cheeks. Then take her straight to the bathroom and watch her brush her teeth. She needs to be broken of this habit, it's not cute, it's not safe, it's bad for her teeth and it's gross.
Take the stand mama, she is young enough that she can be broken of this but you have to take the stand and decide it's not going to happen and make that work for you.