There usually isn’t a setting to disable the trash button or require a more complex delete action. Practical options are:

• Protect important images in playback using the Nikon lock/protect function (key symbol). Protected images can’t be deleted normally.
• If you use both card slots on the D750, set the second card as a backup. Deleting an image in-camera is reported to affect only one card, leaving the backup copy intact.
• You can also lock the memory card with its physical write-protect switch before handing the camera over.
• The simplest real-world approach is to supervise closely, cover the other buttons, and guide your child to use only the directional control during playback.

For complete safety, copy the images elsewhere before handing over the camera. No in-camera method is as foolproof as having a backup.