Follow the BIRD principle to deal with unwanted visitors to your Facebook page
Block a nuisance person from your page. You can also choose to hide their comments. They will still be able to see it but no one else aside from your page admins will.
If you feel behaviour Is getting annoying or repetitive you can ignore it. The best practice is to take the conversation offline. Chances are, if provided with a phone number to discuss grievances, the disgruntled customer won’t call. Yet, it still shows the other customers you have tried to resolve the issue.
Take the conversation offline or into a private message and if you feel its appropriate to reason with the customer.
Comments that’s are extremely unnecessary or potentially upsetting to others can be hidden or deleted from your page. Try not to make a habit of removing posts or comments you don’t like because this can also result in customers thinking you have something to hide and may incite further attacks. However, if you’ve resolved a customer’s complaint and they are happy, you can ask them politely to delete it. Most people will oblige.
At the end of the day, it’s your page and your business. You have the right to remove any comments that you don’t want to affect your brand.