Brain-assisted speech enhancement (BASE) aims to extract the target speaker in complex multi-talker scenarios using electroencephalogram (EEG) signals as an assistive modality, as the auditory attention of the listener can be decoded from electroneurographic signals of the brain. This facilitates a potential integration of EEG electrodes with listening devices to improve the speech intelligibility of hearing-impaired listeners, which was shown by the recently-proposed BASEN model. As in general the multichannel EEG signals are highly correlated and some are even irrelevant to listening, blindly incorporating all EEG channels would lead to a high economic and computational cost. In this work, we therefore propose a geometry-constrained EEG channel selection approach for BASE. We design a new weighted multi-dilation temporal convolutional network (WDTCN) as the backbone to replace the Conv-TasNet in BASEN. Given a raw channel set that is defined by the electrode geometry for feasible integration, we then propose a geometry-constrained convolutional regularization selection (GC-ConvRS) module for WD-TCN to find an informative EEG subset. Experimental results on a public dataset show the superiority of the proposed WD-TCN over BASEN. The GC-ConvRS can further refine the useful EEG subset subject to the geometry constraint, resulting in a better trade-off between performance and integration cost.