Pulling images from another site

[7_Driver]

I have a site (lets call it site A) that pulls all its images from another site (of mine) (call it site B).

So site A, has <img> links to site B everywhere. I'm worried this might look a bit odd (to Google).

I'm thinking of hiding this by setting IIS to pull the contents of a folder on site A from a URL (on site B) - as a permanent re-direct.

That allows the source on site A to always reference site A - yet the images still come from site B. This seems to be totally transparent within a page - it's only if you enter the URL of the image on its own that you get a 301.

If anyone's still following this(!) - my question is - is this worth doing? Should I worry about a lot of img links to another site - and if not, could I be causing more problems than I solve?