It happens if you added a person as a contact fairly recently because you should only allow somebody to remotely control your iPhone if they're trustworthy. The person controlling the screen won't ...

To prevent your iPhone's screen from automatically turning off ... It's Usually Best to Enable Auto-Lock Again Later Although ...

If you wouldn't trust a person to ... in the top-left corner of the screen sharing window, then select Allow Control. Note that you cannot remotely control an iPhone from a Mac or vice-versa.