In this third of three companion papers we assess the utility of column-integrated measurements of CO2 in constraining surface source estimates. The measurements have error characteristics defined by O'Brien and Rayner <2002>. There we described a retrieval algorithm which appeared capable of unbiased retrievals. An assessment of the sensitivity to dominant sources of error in these measurements suggested a precision about 0.5% of the background mixing ratio. We include this information along with the probability of clear sky and the sampling pattern imposed by a particular orbit and scan geometry. We carry out a synthesis inversion to recover specified surface sources. The uncertainty of the inferred sources quantifies the strength of the constraint offered by such measurements. The difference between input and retrieved sources demonstrates biases in the whole procedure. We show that source uncertainties are low in the presence of a sunlit surface but rise dramatically at high latitudes in winter. Provided we use sufficient spatial resolution for the sources we estimate, the inversion can also produce relatively accurate estimates. The inversion procedure is sensitive to biases caused by poor sampling of the diurnal cycle. Errors that isotropically affect all measured mixing ratios do not cause biases in estimated sources.