Actually when you really need to decode a blurred or mosaiced image you can do even more tricks. Especially when they are screenshots. Since you can take a pattern (digits) and blur them with all possible options of certain most popular image editing software, you can then do massive number of comparisons to see what comes out right. It's massively cpu intensive, but I am sure people that need it can do it.

Blacking out the section entirely is the only proper way, since you really want to be sure you are destroying the information in the image, not just dispersing it.

Even then, if you are removing a single digit it can be partially recovered by observing kerning statistics, etc.