An L band geosynchronous synthetic aperture radar (GEO SAR) differential interferometry system (D-InSAR) will be obviously impacted by the background ionosphere, which will give rise to relative image shifts and decorrelations of the SAR interferometry (InSAR) pair, and induce the interferometric phase screen errors in interferograms. However, the background ionosphere varies within the long integration time (hundreds to thousands of seconds) and the extensive imaging scene (1000 km levels) of GEO SAR. As a result, the conventional temporal-spatial invariant background ionosphere model (i.e., frozen model) used in Low Earth Orbit (LEO) SAR is no longer valid. To address the issue, we firstly construct a temporal-spatial background ionosphere variation model, and then theoretically analyze its impacts, including relative image shifts and the decorrelation of the GEO InSAR pair, and the interferometric phase screen errors, on the repeat-track GEO D-InSAR processing. The related impacts highly depend on the background ionosphere parameters (constant total electron content (TEC) component, and the temporal first-order and the temporal second-order derivatives of TEC with respect to the azimuth time), signal bandwidth, and integration time. Finally, the background ionosphere data at Isla Guadalupe Island (29.02 • N, 118.27 • W) on 7-8 October 2013 is employed for validating the aforementioned analysis. Under the selected background ionosphere dataset, the temporal-spatial background ionosphere variation can give rise to a relative azimuth shift of dozens of meters at most, and even the complete decorrelation in the InSAR pair. Moreover, the produced interferometric phase screen error corresponds to a deformation measurement error of more than 0.2 m at most, even in a not severely impacted area.