E-scooter sharing has been commonly used to integrate public transport systems in many cities worldwide. Accurately modeling integration between shared e-scooters and public transport is important for multi-modal urban transportation development and management. However, the effects of catchment size are scarcely considered while modeling their integration by widely adopting the method based on the transit catchment area in previous studies. In this paper, we systematically quantify the impact of the size of the transit catchment area on the integration of shared e-scooters in the public transport system from statistical, temporal, and spatial perspectives. A case study is implemented in Stockholm, Sweden. The results indicate that the transit catchment size has a significant impact on their integration, especially on spatial patterns. This research calls for more attention to consider such catchment size effects to ensure the validity of integration results for urban mobility research and practice.