Well, that’s good, actually. Can you ask your host to elaborate on the “spam” connection? From what we’ve seen so far this looks more like an automated scanning for vulnerable files or a known exploit in some application that also uses an index.php file. If that is the case, this would be a false alarm: even though somebody did try to exploit your index.php, EE would only have given them
Invalid GET Data - Array. The logs only show that a “200” status was returned, which would be consistent with this hypothesis.
If, on the other hand, they have evidence or proof that actual (spam) email was sent using that file, this would change things. Please ask them to clarify.