Turn on broiler, and adjust rack so it is as close to heat source as possible.
In a medium-size mixing bowl, mix together garlic, olive oil, thyme, vinegar, salt and pepper.
Put the mushroom caps, bottom side up, in a shallow baking pan. Brush the caps with 1/2 the dressing. Put the caps under the broiler, and cook for 5 minutes.
Turn the caps, and brush with the remaining dressing. Broil 4 minutes. Toast the buns lightly .
In a small bowl, mix capers and mayonnaise. Spread mayonnaise mixture on the buns, top with mushroom caps, tomato and lettuce.