My vegetable garden is completely off limits to chickens except by invitation. In my opinion, the scratching is even more destructive than the pecking. I have a very small suburban property, but still manage to use the paddock shift system with my ten chickens; each paddock is about a quarter of the available space (mainly
lawn and shrubs) out back, and they stay in the paddocks for 7-10 days. In fact, the only reason I haven't converted my entire back lawn to growing beds is that the lawn is so appealing for chickens!
If you can't exclude them from the veg garden, I would at least keep them out until the plants are very sturdy and strong, and unable to be scratched up; two years ago, my chickens broke into the veg patch and discovered that the
raised bed I built for carrots was the most amazing dustbath ever--not only did I lose every single carrot, they also pitched out half the soil in their enthusiasm.
Edited to add: I see we're neighbours:)