Job searches: do I respond to correct this?

I’m still job searching, and I recently (the end of last week) sent a resume out to a specific employer.

I just got a response via e-mail (standard: we got your resume, we plan to start reviewing in X week and hope to employ someone for the fall semester). Only, it was addressed to a first name that was completely different from mine (my name is Laura. Let’s imagine that it was addressed to Frances - like the name used in the e-mail, Frances is not my first or middle name, or remotely close to my last name).
I can see this being an honest mistake - several resumes have come in, I’m sure, and it was just a matter of typing the wrong name into the e-mail. I’m not in any way offended, but I was slightly confused at first.
Now, there is an option for a response - a statement in the letter that ends with “if this would affect your consideration of the position, please let me know”. The item does not affect my interest in the position from what I know of it. I would consider responding to indicate that it does not affect that, then just ending my response with my actual name and never comment on the error. Or I could not respond and never mention the error (if I were to actually get an interview).

What I don’t think is appropriate would be a response solely to correct the name error. Are my instincts right? Are there any other Wise Doper Thoughts™ on this?