But I understand your concern here. All our lives are now digitalised and maybe stored forever somewhere and anything you do, even if completely benign, could be considered a crime in some country or even in your own country in a few years from now.
(Not trying to make a counter-argument to your comment. I genuinely don't get this part).
I'm not sure how the image is displayed on the parents' device - it could be sent from the child's device, or the image used to compute the hash that the child's image matched could be displayed.
That is different from searching them for illegal material based on what illegal implies at a given time and location.