Tamara,
Sorry for the delay. I'm not sure why that's happening in IE. I've done some investigation, and it appears you're not the only one with this issue. There are multiple reports in the LinkedIn developer area about this happening, but there's not a perfect fix for everyone.
The best I can recommend for now is to try the following change in the /plugins/system/jlinkedsystem/jlinkedsystem.php file. Around line 94, you'll see:
$inJS = '<script type="text/javascript" src="//platform.linkedin.com/in.js?async=true"></script>' . "\n";
Update that by adding https, like below:
$inJS = '<script type="text/javascript" src="https://platform.linkedin.com/in.js?async=true"></script>' . "\n";
Try that. If it doesn't work, even try with http (no s) and see if that improves things.
It's not guaranteed to work, but that's been stated by a few users to fix things up. If not, let us know, and we'll investigate further.
Thanks,
Alex