In most cases no! On long haul flights where you are most likely to use the strap, almost all seats have winged headrests. The straps are attached to these and don’t go around the back of your seat.
See this video on how to attach the straps to a winged headrest.
If the seat does not have a winged headrest, very often there is no screen behind, as it is a budget airline.
If there are screens with no headrest wings, globally this is rare but then it’s only a polite conversation with the person behind before you sit down. You would advise them that you will be sleeping with a FaceCradle, which means you don’t need to recline your seat (they will love that). Suggest they may need help to make sure the strap doesn’t interrupt their viewing, so if it does would they mind adjusting it for you.
If you feel uncomfortable about talking to the person behind, then you will use Modes 1-3 with no problem where your FaceCradle can perform better than a regular neck pillow. For more information, you can view our video on how to attach the strap under "How It Works" and further read our FAQ’s.