I agree with your thinking of putting the food away when you are full. I find that if food is visible than I tend to I pick at it - grazing is not a good thing. It defeats the purpose of having the band. If you think about how many calories you can consume throughout the day by grazing - absolutely you can gain weight. It sounds like you know when it is time to stop, I applaud you!
I am still new to this and trying to retrain my brain. I don't have to finish everything on my plate! I need to stop when I feel full.