Walmart can not claim your donations as a charitable donation on your behalf.

Regardless if a person does or doesn't claim the charitable donation, Walmart never is able to anyway.

There may be other shady aspects about an organization you are donating to and Walmart may be able to make claims on their costs associated with facilitating the donation (for example the costs to set up and maintain the transaction process) but they never ever ever are able to claim your donation, doing so would simply be fraud and there are better ways to cook books than claiming 10 million individual charitable donations on behalf of 10 million people.