Saito obviously knows all the ins and outs of dream sharing and extraction and one would assume he had done his homework on Cobb. This is demonstrated by his consideration of him for the inception attempt and is also revealed when he lets Cobb know that he is well aware of his US immigration difficulties and the charges against him, which he promises to 'fix'.
With these unique insights into both the Cobb character and the mechanics of the dream sharing world and its pitfalls and foibles, it is entirely possible that Saito could have used his influence to explain how Mal's death was not Cobbs fault and may have simply held back on authorising the immigration as collateral for the success of the Fischer inception job.
It is not laid out in any detail as to how he deals with this particular issue but considering how powerful and influential Saito is coupled with his unique insights into the films aspects and concepts then he appears to be one of the only people capable of helping Cobb in this manner.