Integrated localization and communication systems aim to reuse communication waveforms for simultaneous data transmission and localization, but delay resolution is fundamentally limited by the available bandwidth. In practice, large contiguous bandwidths are difficult to obtain due to hardware constraints and spectrum fragmentation. Aggregating non-contiguous narrow bands can increase the effective frequency span, but a non-contiguous frequency layout introduces challenges such as elevated sidelobes and ambiguity in delay estimation. This paper introduces a point-spread-function (PSF)-centric framework for dual-band OFDM delay estimation. We model the observed delay profile as the convolution of the true target response with a PSF determined by the dual-band subcarrier selection pattern, explicitly linking band configuration to resolution and ambiguity. To suppress PSF-induced artifacts, we adapt the RELAX algorithm for dual-band multi-target delay estimation. Simulations demonstrate improved robustness and accuracy in dual-band scenarios, supporting ILC under fragmented spectrum.