How can I delete a picture on Rover after I sent it to the owner?

Go to the client's photo album page. Click on the owner's name. You should see all the pics that have been made public. Hover over that particular one and there should be a "hide" option either at the top or bottom. It can be hidden from public view and won't show up in your reel of canine clients.

It will be visible to you and the client, but not anyone else.