Efficient and secure group writing plays a crucial role in RFID-enabled multi-task backscatter systems. The prior works lay emphasis on the time efficiency of the group data transmission, but neglect its security. This paper is devoted to providing anonymous group writing. We propose the Overlapped Bloom Filter-based protocol (OBF) and its enhanced version (OBF+). The core is to construct an approximately random sequence as a noise by making transmission data for different tag groups overlap with each other, thus hiding the original information with a low computational complexity. The compact filter can guarantee the time efficiency while improving the security of the group writing. To make tags aware of the correctness of the decoded group data, the OBF+ introduces the complementary code-based check mechanism to eliminate the fault data. We prototype the system with USRP and programmable WISP tags, and conduct extensive simulations to evaluate our approaches in terms of the time efficiency, the accuracy, and the anonymity of the data transmission.