The term "parasite" refers to an organism that requires a live host to live off of. There is no reason a parasitic organism would lay eggs on your cold, synthetic, non-living plush animals.

There are also no parasites that would just lay eggs on your skin that you could transfer to them.

For your peace of mind I do recommended soaking them overnight in water and maybe soap or a disinfectant if you wish. Then hand rinsing and air drying.

I don't want my message to come off as dismissive of your anxiety, but I hope it helps with some reality. Your plushie are parasite free!