Walt is partially correct - to have a picture removed entirely, you need to contact Rover support. However, there is another way to keep pics from public eyes (but the owners will still be able to see them).
Go to the dog profile area of a client, current or past. This is NOT the scrolling picture diary that says "Photos of Rover's stay." On a PC, it's in the lower left and lists the owner's name and the dog's name.
Click. A screen will open that says "Rover's Photo Album." All pictures ever taken of that dog, regardless of sitter, will appear.
Hover over any photo that you have submitted and you will see 'hidden' or 'unhidden'. Click on any photo and you will have the choice to 'hide' or 'unhide'.
Since it only shows the last 50 pics posted, I use this feature to hide all but the best 1 or 2 photos from each stay. This way more different dogs are visible when clients are clicking through the pics of my past guests.
You cannot hide or delete photo's that you have sent to the client. You must contact support@rover.com and they will hide/remove the for you. It's a good idea to attach the photo(s) to the email so they know the exact photo's you want them to handle.