I think it's an unnecessary level of noise, but I think it's just that: noise. Writing one or not writing one doesn't send any signal either way at this stage.

I think it's an unnecessary level of noise, but I think it's just that: noise. Writing one or not writing one doesn't send any signal either way at this stage. If it puts your mind at ease, write a perfunctory one and bcc the recruiter so he shuts up about it.