Prepare a grill for indirect heat. If using a charcoal grill, build the hot coals on one side only. If using a gas grill, heat one side only to medium-high heat.
Bring a large pot of salted water to a boil. Add the green beans and cook at a rapid boil until tender, 2 to 3 minutes. Transfer the green beans to an ice bath, then dry on a kitchen towel.
Add the green beans to a grill basket and place over indirect heat to char them slightly, about 5 minutes. You do not have to cover the grill. When they reach the char level you are looking for, transfer them to a serving platter.
Whisk together the lemon juice, garlic, mustard and oregano in a medium bowl. Slowly drizzle in the olive oil while whisking constantly, then season with salt and pepper.
Pour the oregano vinaigrette over the green beans while still warm, then sprinkle with the feta and almonds. Serve warm or at room temperature.