lol, your username is cool. :D
They might heat them if they are small enough, it depends on the betta.
My bettas tried to eat the snails that hitched a ride on the hornwort I got, but they couldn't get to them because the snails had trapdoors.
I believe one of them in my CT tanks was either eaten by him or just died because I couldn't find it. Though I believe it had enough food so my betta probably ate him.
If you want to get rid of them, you should always check for the eggs and squish them onto a paper towel and toss in the trash.
The snails themself, well, they are probably the kind that populates super fast so you could crush them against the tank if your bettas don't eat them. This I assume kills them fast so they don't feel much.
If you want to keep them just keep a very close eye for eggs, they will reproduce on their own, at least the ones I had did!