We spoke to Courtney's parents, Deborah and Kim Clenney, for a new 'TMZ Investigates' airing Monday at 9 PM ET/8 Central on FOX ... when the question of a slur Courtney used during an argument with Christian came up.

As we previously reported ... Christian secretly recorded Courtney calling him the n-word repeatedly during a fight months before she killed him in the Miami condo where they lived together.

The audio's brutal to hear ... and also explainable according to CC's parents -- who are now facing criminal charges for allegedly illegally accessing Christian's computer after he was killed.

We spoke to them before the arrest -- they have never spoken publicly before -- and they told us Courtney said she needed to use such a horrible slur because she was trying to get Christian to leave, with her mom Deborah claiming Courtney said no "self-respecting Black man would stick around after being called that name."

Deborah went on to say Courtney liked Christian partly because he was Black ... and she doesn't think their daughter would have been prosecuted if she were Black or if Christian were white.

Clenney pled not guilty to second-degree murder after stabbing her boyfriend in the chest ... her parents tell us she will plead self-defense.