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.
Valid point, it's not a network rule, although it may become one at some point.
Still it's a good practice accepted nowadays in most of the "banks" and post offices - not to accept dirty receipts, which exposed those MtGox vulnerabilities.
The problem is, there is indefinite ways to alter a cheque without invalidate it. We need to live with transaction malleability and actually it's no big deal