The basic idea of the Tospfot R"id [Rav Isaiah, one of the baali Hatospfot] is that barter would work to acquire a wife if the handkerchief has a penny's worth. His point is: the only thing the Gemara really means to exclude is exchange when one of the objects being exchanged is less than a penny.

This is why Rav Shach is dividing between two kinds of exchange in order to answer for the Tospfot R''id. If it has a penny's worth then it comes under the category of acquiring by means of money. Only when the handkerchief is less is it actually kinyan Sudar which would not acquire a woman.

This answers my question I asked yesterday that the Gemara is interested in eliminating exchange and does not mention kinyan sudar (acquire by exchange of a  handkerchief).

My point today is that kinyan sudar in the view of the Tosfot R''id is in fact a kind of exchange but even exchange is ok if it is more than a penny.
And that is in fact the way Rav Shach answers the questions of the Tospfot R''id