What is the grammatical structure of: 我把你们带到茶馆来。
Here unfortunately, 来 doesn't indicate completion. Instead, it indicates direction of an action.
我把你们带到茶馆来=我把你们带来茶馆（indicating that the speaker's location is (or was, depending on context) 茶馆）
Comparison:
我把你们带到茶馆去=我把你们带去茶馆（indicating that the speaker is not at 茶馆）