not give (something) another thought
To not concern oneself with or worry about something any further. A: "I'm so sorry for breaking that vase!" B: "Oh, don't worry, it was just a cheap old thing. Don't give it another thought!" I wouldn't give her comments another thought—she's just trying to hurt your feelings because she's jealous, that's all.
not give it another thought
not to worry about something anymore. (A polite way of accepting someone's apology.) It's okay. Please don't give it another thought. You should not give it another thought. No one was bothered at all.