I've never had a transitional object from a T but it makes sense to me how it would work for some people. People exchange gifts and things with symbolic meaning, I don't think it is very different with a T, more just one-sided. If I wanted such an object from a T, would probably say that I would like to have something symbolic that reminds me of them and I can keep with me, and let them choose. I would think their choice of object might also be meaningful in terms of how they see me and our relationship. E.g. do they choose something generic/relatively impersonal, something that represents me, or them in a more specific way?