Hey randommike,
That's a great question! Relocating the backup file could damage the contents and cause the file to become unusable. You could allow the backup to complete, then copy the file to the external drive, and then delete it from the C drive. If you ever needed to restore from it, you would need to move it back to the original location. Those details can be found in the guide you recently viewed under the sections "Find backups stored on your Mac or PC" and "Delete or copy backups on your Mac or PC". Here's the link, just in case: Locate backups of your iPhone, iPad, and iPod touch - Apple Support
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Take care!