<p>We examine the role of nonlinear aspects of the Compton effect in the development of narrow-band gamma-ray sources based on the interaction between electron beams and laser pulses. The study focuses on parameters relevant to the ongoing project at the National Center for Physics and Mathematics (NCPM). We present estimates of photon yield and relative spectral width, along with an assessment of how laser and electron beam parameters influence these characteristics. The study primarily focuses on the weakly nonlinear regime of the Compton effect, where light pressure on electrons is significant but not dominant, and quantum effects are negligible. We employ both analytical calculations and numerical modeling to describe gamma-ray generation processes and to optimize system parameters. The potential for investigating the strongly nonlinear regime within the framework of this project is also discussed. The results obtained contribute to the development of highly efficient narrow-band gamma-ray sources.</p>