Welcome to Fishlore.
My opinion on the common pond snail (the one that is most likely to be a plant hitchhiker) differs a bit from others. I have them in all but one of my tanks (and that one is only snail free because one of its previous inhabitants methodically ate the snails), and I have come to like them.
They are a bit of an eyesore if allowed to overpopulate, but the only way they'll overpopulate is if they're given the food to do so. I know that one of my tanks has an excess of
detritus on the bottom because the snails have gone nuts in the past week. Some thorough vacuuming will solve the problem in short order, and the snail population will return to a more reasonable level.
To rid plants of snails before introducing them (sorry, this doesn't help your current tank), you can use a mild bleach dip (can harm some plants) a potassium permanganate dip (not harmful to plants, though it will stain the rug, furniture, and possibly your hands, purple), an ice bath (again, can harm some plants) or a salt bath (yep, can harm some plants). PP is the safest for the plants, but requires purchasing a chemical you likely don't have in your house.