This paper proposes a neural-network-assisted deformable matched filtering (DMF) framework for carrier-less amplitude and phase (CAP) modulation operating under bandwidth-limited channel conditions. Instead of replacing the analytically derived CAP matched filter, the proposed receiver learns a residual deformation of the nominal matched filter based on a compact set of physically motivated signal features extracted from the received waveform. A total of 16 time-domain, frequency-domain, and memory-related features are used to provide a low-dimensional representation of bandwidth-induced pulse distortion. These features are mapped by a fully connected neural network to complex-valued matched filter coefficients, enabling adaptive pulse-shape compensation prior to symbol-rate sampling. The network is trained end-to-end using a differentiable loss function based on error vector magnitude (EVM). Experimental results obtained using a hardware-in-the-loop CAP transmission system demonstrate that the proposed DMF significantly outperforms conventional fixed matched filtering under severe bandwidth constraints, without requiring decision feedback or increasing receiver latency.