Manipulating fragile objects in environments such as homes and factories requires stable and gentle grasping along with precise and safe placement. Compared to traditional rigid grippers, the use of soft grippers reduces the control complexity and the risk of damaging objects. However, it is challenging to integrate camera-based optical tactile sensing into a soft gripper without compromising the flexibility and adaptability of the fingers, while also ensuring that the precision of tactile perception remains unaffected by passive deformations of the soft structure during object contact. In this paper, we demonstrate a modular soft two-fingered gripper with a 3D-printed optical tactile sensor (the TacTip) integrated in the palm. We propose a soft-grasping strategy that includes three functions: light contact detection, grasp pose adjustment and loss-of-contact detection, so that objects of different shapes and sizes can be grasped stably and placed precisely, which we test with both artificial and household objects. By sequentially implementing these three functions, the grasp success rate progressively improves from 45% without any functions, to 59% with light contact detection, 90% with grasp pose adjustment, and 97% with loss-of-contact detection, achieving a sub-millimeter placement precision. Overall, this work demonstrates the feasibility and utility of integrating optical tactile sensors into the palm of a soft gripper, of applicability to various types of soft manipulators. The proposed grasping strategy has potential applications in areas such as fragile product processing and home assistance.