Preheat an outdoor grill to medium-high heat. Cook the pasta according to the package directions. Drain and let cool.
Brush the corn, yellow squash, zucchini, bell pepper and scallions lightly with oil and season lightly with salt and pepper. Grill the corn, turning frequently, until cooked through and the kernels are charred, about 10 minutes. Grill the zucchini and squash slices, turning once, until charred but not mushy, about 2 minutes per side. Grill the pepper slices until they are charred on both sides, about 3 minutes per side. Grill the scallions whole, turning them frequently, until charred and soft, about 2 minutes.
Meanwhile, in a large bowl, whisk together the pesto, olive oil, lemon juice and zest. Season to taste with salt and pepper.
Cut the yellow squash, zucchini and bell peppers into 1/2-inch pieces and add them to the bowl with the dressing. Cut the kernels off the corn and add them to the zucchini; chop the scallions and add them, too. Add the pasta and grape tomatoes and gently toss until everything is coated with the dressing. Add the parsley, toss and season to taste. Serve at room temperature.