You can only delete a photo from a challenge within 5 minutes of submitting it! - (updated 01/17/18)
After that, you will need to swap the image.
To delete a photo, hover over it with your mouse in the 'Top Photographer' ranking (the default when you go to any challenge).
A "Trash Can" icon will then appear and pressing on it will open a 'remove' button.
Press the button and the photo will be removed.
*Note*: You can still delete the photo from your profile at any time.
Deleting a photo from your profile does not remove it from the challenge!