“In a response to” also works, but it has the same quote connotation for me that “in a reply to” has. I think “in response” feels like an established term to me that has a separate meaning from “in” + “response,” so substituting “reply” for “response” doesn’t work for me.

Interestingly, although the Cambridge dictionary includes references to each (meaning “in reply to” is formally accepted English [funnily enough, I can understand the second usage there, for very formal written correspondence]), there’s only a full page for “in response to.”