I had all my pets look at the comet, and my Amber Zenirix accidentally got the Stardust Effect.

You can't completely remove it from the pet, but you can disable it so it won't show. Click on the pet's image, then at the bottom of the pop up you'll see a drop-down list where Stardust will be selected. Click on it and choose "None", then Apply Chosen Effect~

Ah, thank you!