I can't tell from the picture, but if you have live plants in the tank, snails will often be attached. For future reference, when you buy live plants at a shop, rinse and run your hand across the leaves to detach any snails and eggs back into the plant tank.
Snails multiply easily and quickly, so I would remove them now if you don't want lots of snails. They shouldn't harm the betta, but they can overrun the tank. This tank already looks like it's under 5 gal (the recommended minimum size for a betta), so take that into consideration if you want to keep them or not.
Snails are not all bad. They are good for eating decaying plant matter and such things, keeping your aquarium clean. (I tried a zebra snail for a while, but my betta hated him and chipped his shell. Back to manual algae cleaning for me!) The more food the snails have, the quicker they'll grow and reproduce. To keep the snails, you'd have to be very careful with tank maintenance (no overfeeding, manually clean up decaying matter, etc.).