Off-axis three-mirror anastigmat (TMA) telescopes provide excellent correction of aberrations over a large field-of-view in one direction. In a push broom configuration, this lightweight and compact optical configuration enables high-performing imaging. Moreover, passive multi-spectral acquisition can be achieved using a filter stack positioned at the detector vicinity. Stray light is a typical limiting factor for instrument performance and its control is specific to the type of optical configuration. We describe the stray light control and analysis methods in an off-axis TMA. The design intends to control first-order scattering from non-optical surfaces and to block straight shots. This is achieved through usage of elements such as apertures and baffles, both internal and external to the instrument. It will be demonstrated that the aperture stop is a critical element, whose stray light contribution can be controlled with V-groove vanes. Impact of mirrors roughness, a manufacturing physical limitation, is evaluated by modeling the bidirectional scattering distribution function and computing the stray light distribution at the detector for point-like source illumination. We show that the scattering on the different mirrors broaden differently the spot size, as the successive mirrors focus or expand the scattered rays differently. Finally, the ghost reflections inside the filter stack are evaluated and we show that there is no cross-talk between the different channels.