It didn't change in your Word, and it didn't change in the document or template. It just means that, somehow, the logo-file isn't accessible for people using the remote desktop, only if you use the real desktop. Anyway, that's what I understand from your post; it's not very clear, alas.
The guy who made the document with the logo and the guy who setup the remote desktop together will be able to find out the cause and remedy it, I trust.
I've never seen this before but after logging in to my computer from home through remote desktop for the first time a couple days ago, something has changed in Word. The logo on my company letterhead has disappeared and a little box with a red x is now in the place where the logo used to be.
Anyone have a clue what happened to my program?