Open Messenger
Open the chat with the person
Tap their name at the top
Tap Privacy and support or Privacy
Tap Block
Choose Block on Messenger or Block messages and calls
Confirm the block
If needed, open Facebook
Go to the person’s profile
Tap Friends
Tap Unfriend
Confirm the unfriend
If you only want to remove the chat, go back to Messenger
Long-press the conversation
Tap Delete
Confirm deletion