thermodynamics - Clarification on Clausius Inequality

Consider a heat reservoir which gains heat $Q$ irreversibly at temperature $T$ from the surroundings which is at temperature $T_0$. The entropy change of reservoir is then given by $\frac{Q}{T}$, while that of the surroundings is $-\frac{Q}{T_0}$.

My question is, how is this possible? According to the Clausius inequality, the entropy change of a irreversible process is greater than that due to heat transfer. Please help, thank you!