Anyone else's ex do the thing where they bad-mouth you to the kids?

Been noticing my 10yo repeating things about me that are just... untrue. Or exaggerated. Like "dad never helps with school stuff" when I literally just helped him with a whole science project.

I know I'm not supposed to do the same back but ngl it's infuriating. How do you handle this without dragging your kids into adult conflict? Do I just calmly correct it every time or am I overthinking?