I have an old reference book with two ISBNs listed inside the front cover. One ISBN is for thumb index. My book has the thumb index indents but the little labels have all fallen off. So if I  post it to the thumb index ISBN, the requestor might reasonably expect the thumb index to be usable, which they are not since the labels are gone. 

So should I post it to the non-thumb indexed ISBN or go ahead and post it to the thumb indexed ISBN and then tell anyone who requests it that the index stickers are gone?

You should post it to the ISBN that matches binding. So post to the thumb index ISBN.

I think you should probably let any requestors know that the labels have fallen off, and make sure they still want it. It sounds postable to me, but the labels falling off is maybe a gray area.

What Sara Said