Bill19542: As far as I can see, you can't buy an avatar in the mobile game but you can in the PC version which screams out to me that if it's bought on the PC version, it will only work on there.
Exactly. This falls into the same category as "apparel", which is available only on mobile and only applies to mobile. It does not apply to PC.
So, anyone that bought an avatar on PC expecting to use it on mobile, should check with CS, if they do not want to use it on PC. Otherwise, I don't think there is anything else for WGT to do.