Buyers won't know that you turned off or on Best Offers unless they look at your listing. They don't receive a notification if you discontinue or list using Best Offer.
If you are referring to "listings eligible to send offers" that eBay sends, you can't turn that off but you can ignore it.
The only time buyers get an offer notification is when you send them through"listings eligible to send offers".
Keep in mind, not all buyers accept offers sent by sellers.
