For an off-axis source, the telescope's effective area becomes smaller. For Wolter telescopes, this effect is mostly due to decrease of reflection efficiency for non-optimal grazing incidence angles. This effect is called vignetting and it is well-known for photography.
The effect of vignetting strongly affects the spectral analysis of extended sources as local background subtraction technique gives the stronger bias the more extended region (by comparing with field-of-view of the instrument) is analyzed. To handle with such a bias, a special technique is to be used. The commonly used technique is based on subsequent rescaling of background spectrum due to comparison of count rates at highest (e.g. $> 10$ keV for EPIC camera on-board XMM-Newton satellite) energies. Note that this technique also introduces some bias as the vignetting is generally energy-dependent (so, generally, the correction of spectral slope is also required). However, it is a second-order effect and thus can generally be neglected.