Many professors will share what they write with students even when the expectation is that they are "confidential". I don't have a problem with it as long as the recommender is honest and independent.
I think people might fear that only positive statements will be shared, somehow indicating bias toward the positive. But if a professor feels they need to write negative things, then they really should talk to the student about it before writing/sending any letter. If the professor can't support a student they should be advised of that. It is a way to avoid misunderstandings.
The response could be "thanks", or "thanks but that isn't necessary". Your call.
I was told, years after graduation, that my professor wrote me letters of recommendation, which he didn't share, that he intended to be entirely positive, but the phrasing could be interpreted otherwise. The person who told me (a colleague of the professor) said that it probably caused me a setback. In essence the advisor said that I was probably the world's foremost expert on a topic that some would consider very minor. He meant well but there were some cultural (math culture, actually) considerations that he didn't recognize. Even if he had shared it with his colleague, rather than myself, I might have had a different career trajectory. Just a misunderstanding, but with serious consequences.