"You don't need reminding OF that." -- OR -- "You don't need reminding." It means that the person does not need to be reminding of/about something.

Hello Aminotvxq, I would think it means that you don't need to be reminded of something that was said before. Example: You don't need reminding that you should take out the garbage (means I should not have to tell you/remind you). Keep on learning! Regards, David