Preheat grill to medium-high heat (400°F to 425°F) for indirect grilling. Prepare crust as directed on package. Place on heavy duty foil sprayed with no stick cooking spray. If necessary, press out any folds or creases. Brush crust with about 1/2 of the beaten egg white.
Mix sugar, cornstarch, cinnamon and ginger in large bowl. Add fruit and vanilla; toss gently. Spoon into center of crust, spreading to within 2 inches of edges. Fold 2-inch edge of crust up over fruit, pleating or folding crust as needed. Brush crust with remaining egg white. Place tart and foil over unlit burner. Cover.
Grill 20 minutes or until crust is golden brown, rotating tart and foil after 10 minutes. Cool slightly before serving.