Like XenForo 1.x itself, add-ons for XF 1.x are in support mode. This means that they will receive bug fixes until May 31st, 2019 and security updates only until December 31st, 2019. They are feature locked and no new features will be added. As of December 31, 2019 they will be End of Life and no further updates will be given after that date.
After you download and install the update for the IMPORTER, you need to uninstall the actual Social Group add-on and re-install it. This will reset the database tables for the social group system to an empty state.
Then run the importer again, and if prompted select 'Start a fresh import' and click 'Restart'.
Unfortunately, the site that donated a clone of their site to develop this add-on did not have any group avatars that I could test an import with. So, I couldn't include an importer for the group avatars with a clear conscience.
That and I do believe the size of the avatars would be in question. At this moment I don't have access to my development server because I'm currently transferring everything to a new server (about 200GB so it will be a while). But I think the group avatars in vB are fairly small and would look horrible when stretched to the size used by the group system. As soon as I can access everything again, I'll double check that.