This paper discusses compensation strategies for the aberration fields caused by the error in the radius of curvature (ROC) of the primary mirror (PM) in pupil-offset off-axis three-mirror anastigmatic (TMA) astronomical telescopes. Based on the nodal aberration theory framework, the specific astigmatic and coma aberrations of the off-axis three-mirror system in the presence of the ROC error of the PM are derived. It is demonstrated that some field-dependent aberration components can be induced by ROC error in the off-axis TMA telescopes, apart from the dominating field-constant aberration terms. To reduce the influence of the ROC error on the aberration fields, we propose two aberration compensation strategies: adjusting the position of the PM and introducing axial misalignment of the secondary mirror (SM). Through theoretical analysis and simulations, we conclude that the compensation strategy of changing the axial position of the PM can make the aberration distribution close to the nominal state; the compensation strategy of axially adjusting the SM can make the aberration distribution meet the observation requirements, which is more suitable for space applications. We also discuss compensating the effect of the ROC error using lateral misalignments.