Essentially, you stop giving into the whining. I can eat breakfast at the table, and our BTs don't bother me at all, but let my husband sit down with a bowl of cereal... well, let's just say they can sense an easy mark.
It may take a week or more, but if you make an effort and don't give them anything when you are eating your own food, they will eventually get it through their heads that you're not worth bothering with. Whining for their own treats is another issue, but I'm sensing they are bumming your food, not theirs!
If you have to, isolate them in another room while you eat or have a snack. Their treats should be fed at predictable intervals; for example, after they go out for their duties, after they eat their own meal, etc. Good luck.