Sentence examples for that matter from inspiring English sources

"that matter" is a correct and usable phrase in written English.
It can be used as a noun phrase that refers to a particular subject or issue being discussed. An example of using "that matter" in a sentence is: I don't want to discuss the details of our argument, but I do want to address one thing: your lack of communication. That matter needs to be addressed if we want to move forward in our relationship.