hey fred,
some versions ago there was a new option introduced to save a copy of the external image directly on your server.
to enable it go to your easysocial backend -> settings -> links and set cache images to "yes".

on our end this definately improved the overall perfomance, but even more important than the file size is that you're no longer depending on the external source. from bad days I can tell ya that some external sites had removed the image that was shared on our sites and then our site was nearly unusuable as the server still tries to get a connection...

hope that helps and have a nice day

Now when that stores the image to our local server does that compress it as well?

hey fred,
don't want to give you false informations but I think when storing a copy on your server then there's no compression done. (at least comparing some new link pics on my end with the original pics they all had the same size).

however as you then have full control as they're on your server you can of course apply your own image optimization, but as said even more important you no longer have to rely on the external source because the worst thing that can happen in terms of load time is that the original source is not available.