"Mete out" synonyms: dish out, administer, allot It basically means to utilize to something else. It's not a word I use or hear often, so I'm not entirely familiar with the word. I think the only times I hear it are in situations with the law or justice. "Brand of justice" is one own's definition of righteousness. Vigilantes are often mentioned when it comes to the subject of someone's brand of justice.

to 'mete out' means to allot or apportion a punishment or reward. 'its brand of justice' is a way of the writer saying that it is a form of justice considered appropriate by the authorities in question, but the writer, or the intended audience, does not agree. So in some countries, execution or flogging is considered appropriate punishment, but many others would not agree with this. So here, 'brand' means a particular type.

Mete means to give out or administer Brand of justice simply means the type of justice