In this article, we present an adaptive busing-table service (BTS) gripper. The BTS gripper is a mode-changeable three-fingered parallel gripper with compliant linkage-based finger mechanisms and has two modes: adaptive grasp and nongrasp modes (push/pull operation). For the BTS task, the gripper must be able to grasp dishes of various sizes, shapes, and weights. In addition, the gripper must have the capability to push and pull dishes so that there is sufficient space for holding the dishes. A compliant linkage-based finger mechanism using mechanical compliance and a stopper was developed to implement adaptive grasping. A mode-changing mechanism and rigid posture of the finger with a mechanical stopper were designed to achieve the nongrasp mode. A gripper prototype was designed, and the feasibility and effectiveness of the proposed gripper were verified through several experiments on various dishes and objects on a 1-DOF jig testbed and 6-DOF manipulator. Thus, this study contributes to the advancement of robotic manipulation technology by offering a novel gripper design for complex BTS scenarios.