If you can identify the request which generates the response with the errant reference to http://mysite.mydomain.com/it/sites001/_vti_bin/owssvr.dll?XMLDATA..., you could use a stream profile and STREAM::expression basd iRule to rewrite the references to https://... You can check the STREAM::expression wiki page for examples.
I would also think that there is a method for instructing the application that it's being proxied by an SSL offloading device and to use https:// references even though it's answering on http://. The method for doing this in Exchange is to insert an HTTP header "Front-End-Https: On".
Aaron
Nimbostratus
