[mothered]

Worked perfectly. The only question they asked was:
"Was the package was open or was it damaged while it was delivered?"
And I responded
"The outer package was not open. The inner package is dirty and did not come sealed shut and was crushed a bit"

Good work with your response and of course, the SE Itself.

They told me to return what I received for a full refund.
Now my question is can I get away with keeping the wireless receiver? Or should I return everything except the mouse and try to buy a separate receiver.
I told them upon opening the package the mouse was missing but didn't elaborate.

Why go through the hassle of purchasing a receiver?

Just keep It.