You will have to have a way to make sure the parent has actually given
permission. I am assuming you would have to have an email or something
from the parent.
Depends a little on which Moodle you have. This idea is for 2.8.
Set up a group specifically for this activity. Do not add the student's name to this group until you have received permission from the parent. Then when you create the URL link, go to the Restrict Activity section and add access restriction of Group and choose the group you have set up. Students will not be able to view this activity until they are in the group.
Hope that helps.