However, some of the cheques issued by gox have dirt on them. Some customers cleaned the cheque first, then sent to Bitcoin Bank and got paid. The related gox bank account is then emptied.
One important point here is that this all was fine, as long as banks accepted both dirty and clean receipts, and dirty receipts issued by gox were actually more likely go to the bank, because all receipts are actually sent by post, and it would take significant amount of effort for the customer to intercepts those receipts and modify them.
But at some point banks have changed their policy and decided not to accept dirty receipts to prevent some forms of fraud. They simply throw them away. And that's when some customers were able to collect those rejected recepts, clean them and re-submit to make them processed (unnoticed by Gox).
A cheque with valid signature, no matter dirty or clean, is a valid cheque.
The Bitcoin Bank is a decentralized bank. Anyone with a mining rig could become part of the bank (miner). Some miners do not like dirty cheque (although they are still valid), so customers have to manually clean the cheque before they could cash it. However, this is really up to the policy of each miner.