The snack is not a prize
Dessert or a favourite snack does not have to be payment for eating dinner. That bargain makes the dinner food feel like the obstacle.
Serve the snack because it is snack time
Serve the meal. Later, serve the snack because it is snack time.
“Three more bites and you get the yogurt” teaches them the dinner is the toll. The yogurt can simply be the next food on the clock.
If milk is an allergy
Yogurt and cheese cannot be the prize, the snack, or the sprinkle. They stay off. Use a food they already eat that is free of milk.
A safe fruit is a fine snack. It does not have to be earned.
What you say at the table
Talk about the food that is there. Skip the countdown toward a reward.
If they leave food, the snack still comes at snack time, in its usual size. You do not supersize it to compensate, and you do not cancel it to punish.
A sentence you can say
“Yogurt is at snack time.”