Task-oriented communication is a key enabler of emerging 6G systems, where the objective is to support decisions and actions rather than full message reconstruction. From an information-theoretic perspective, identification (ID) codes provide a natural abstraction for this paradigm by enabling receivers to test whether a task-relevant message was sent, without decoding the entire message. Motivated by the strong impact of feedback on ID and by the growing interest in integrated communication and sensing, this paper studies joint identification and sensing (JIDAS) over state-dependent discrete memoryless channels with noisy strictly causal feedback. The transmitter conveys identification messages while simultaneously estimating the channel state from the feedback signal. For both deterministic and randomized coding schemes, we derive lower and upper bounds on the capacity--distortion function. The results quantify the fundamental limits of JIDAS under noisy feedback and recover existing noiseless-feedback characterizations as special cases.