This paper describes our submission to the Second Clarity Enhancement Challenge (CEC2), which consists of target speech enhancement for hearing-aid (HA) devices in noisy-reverberant environments with multiple interferers such as music and competing speakers. Our approach builds upon the powerful iterative neural/beamforming enhancement (iNeuBe) framework introduced in our recent work, and this paper extends it for target speaker extraction. We therefore name the proposed approach as iNeuBe-X, where the X stands for extraction. To address the challenges encountered in the CEC2 setting, we introduce four major novelties: (1) we extend the state-of-the-art TF-GridNet model, originally designed for monaural speaker separation, for multi-channel, causal speech enhancement, and large improvements are observed by replacing the TCNDenseNet used in iNeuBe with this new architecture; (2) we leverage a recent dual window size approach with future-frame prediction to ensure that iNueBe-X satisfies the 5 ms constraint on algorithmic latency required by CEC2; (3) we introduce a novel speaker-conditioning branch for TF-GridNet to achieve target speaker extraction; (4) we propose a fine-tuning step, where we compute an additional loss with respect to the target speaker signal compensated with the listener audiogram. Without using external data, on the official development set our best model reaches a hearing-aid speech perception index (HASPI) score of 0.942 and a scale-invariant signal-to-distortion ratio improvement (SI-SDRi) of 18.8 dB. These results are promising given the fact that the CEC2 data is extremely challenging (e.g., on the development set the mixture SI-SDR is -12.3 dB). A demo of our submitted system is available at WAVLab CEC2 demo.