Neither Inventory check links nor Reconcile will update the Transaction Source field. This is a common error that usually occur when a posting corruption occurs resulting with incomplete and incorrect records. Though, no harm from trying.
Before thinking of what's the best solution criteria, I recommend checking the other Inventory tables as will as GL for any potential errors. Posting corruption might affect other tables or GL posting, therefore, it is a must to check them all. Quantities and cost is a priority.
In case your issue is limited to the transaction source, updating the field in IV30300 is safe as you can retrieve the TRXSORCE value from SEE30303 and GL20000. Although, I don't recommend such hard-coded solutions.I recommend reversing the transaction with the required corrective adjustment. Keep a reference for auditing purposes.
Please provide us with your feedback to provide further details in case the error is not limited to the transaction source field.
Best Regards,
Mahmoud AlSaadi