I don't want visitors in Pokemon amie because I don't like seeing presents piling up on the screen and I don't want to keep having to open them. Is there a way to prevent visitors from showing up?
Just keep your bottom screen off the amie screen. Keep it on the Super Training or PSS one and you will receive no gifts.
There is no way to prevent visitors. I know it may be annoying to you, but that's just the way Game Freak designed it.
Keep putting Pokepuffs there. It resets the visitors or something as it says in the message.