In general, it is much safer to ask a website's permission than to assume anything.

From the "Nominate Your Pet" page
Â_Â_Â_ All material submitted becomes the property of Pet of the Day and all copyrights are assigned to us. This is to protect us and prevent others from reusing your work. You do, however, retain the rights to your material for your own use.
You can print out a Pet of the Day's picture, hang it on your fridge, use it for your personal background ... anything that's for your own personal use.

You cannot sell a CD of our images, post them on your own site without attribution, linking, or permission, pretend they are your images, print them on a poster or in a book without permission, or anything else.

The other site took the time to erase the CatoftheDay award plates from these cat's images, so we know THEY know they were doing something wrong.