Whisk the oil, vinegar, garlic, thyme, and lemon zest in large bowl. Add the radicchio and toss. Marinate for 5-10 minutes.
Bring a grill or grill pan to medium/high heat. Remove the radicchio from the marinade, letting the excess run off into the bowl. Place the radicchio on the grill and sprinkle with salt and pepper; reserve the marinade for later. Grill the radicchio, turning once or twice, until it has darkened and the edges are slightly charred and crispy, about 5 minutes.
Transfer radicchio to a serving platter. (The wedges may separate: this is ok.) Top with crumbled cheese and grapes, and drizzle with reserved marinade. Garnish with extra thyme for color. Serve warm or at room temperature.