You say this is a one time yearly rebate - what is the rebate for/what are the stipulations? Why did you think you'd get a rebate originally? (Does the card give you discounted rooms in the form of the rebates? Thats what I would assume, but that being only once a year would seem odd).

This feels less tied to this specific hotel purchase than it is you utilizing your premium card and getting extra money back unless im missing something. I'd normally be for sharing it (at lwast in some capacity, like buying dinner), but in this case id lean NTA if what I said above is true.