Regarding the question of why TL doesn't get to put her own expiration date on it, let me submit the following (this may or may not be the case in this particular situation, but it does still illustrate my point).
If the donation had been an actual voucher or something from the deli that had an expiration date on it from the deli itself, would TL be in her rights to put her own expiration on it instead? No. She doesn't get to do that. She, as the middleman in the donation process, doesn't get to impose just any old deadline on it that she wishes.
Had she not picked the dinner up, would the deli have honored Sister's claim to it? We don't know now. I'm interested in knowing. But I suspect that, if this were all done on the level (which I'm increasingly suspecting wasn't the case here) and this were a true auction item that the deli was aware of, they would have honored Sister's claim to the dinner - even the day after Thanksgiving. That's an assumption on my part. And not one that may be true. But that's between Sister and Deli. Only.
Regardless of any of the other details, though, the plain and simple truth - regardless of any of the suppositions we're making and/or facts we actually know - is that TL has no right to the dinner after it's donated. At all. Whether it means that the dinner ended up not being claimed, went to waste or whatever. Her claim to it was over and she cannot, in any way, shape or form, go get said dinner for herself, a food kitchen, the neighborhood cat or the man on the moon.