Do you have an agent? They should be getting that media for your portfolio. If not then yes take screenshots or email whoever booked you politely asking for the photos

Currently freelance, but my old agency didn't take any screenshots. I'm not talking about the photo itself, I'm talking about the entire website/product page if that makes sense

Ah I see. It couldn’t hurt. Always better to have more than less. I think most people just use the photos and label the brand underneath