Hi Kim,
This is a natural part of the way a bird eats. In the wild, if food is abundant, the birds will eat their favorite bits and discard the rest. This helps plant the environment and also feeds some ground dwelling animals. In captivity, we tend to give our birds too much food, so they exhibit the same feeding behavior. While it is important that they always have food available, you don’t have to give it all to them at once. I would suggest offering fewer berries at a time and once they eat those, give them more. As long as the berries have not become soiled with feces, you can put them back in the dish. If they learn you are just going to put them back, they will be less likely to waste them. You can also try a large shallow dish on the cage floor for them to eat out of. Budgies are ground feeders in the wild, so this is a natural way for them to eat.
Thank you for asking Lafeber,
Brenda