This option is turned off by default, and will only be on if you’ve previously changed your iPhone’s settings. Read receipts do not work with SMS text messages. The switch for Send Read Receipts will disappear from the Messages menu if you turn off iMessage.
If you find yourself in a conversation that you don’t want to edit Read Receipts for, tap the back button in the upper-left corner of the screen.
If you don’t see the Send Read Receipts button here, that means your contact does not have an iPhone, or is not using iMessage. If Send Read Receipts is already in off position, then Read Receipts are already disabled for this contact. Your other contacts will still receive read receipts from you if you have “Send Read Receipts” turned on in your Messages settings. [1] X Research source