I have built a website for a client who specifically asked

I have built a website for a client who specifically asked for it to work perfect in IE8 as many of their visitors still use it. I've tried my best but keep getting notifications that it's not working properly in IE8. Especially the floating cart.
Now for the strange part: I can't reproduce their issues in IE8 anywhere. I've tested it in Browserstack, it turns out fine. I've tested it on old computers, all looks good. I've asked others to test it, no problem.
One of the people working for the company has tested at her home, and again, it all looks good.
So the problem seems to occur only inside the company building. I've asked them to refresh their cache and see if it's possibly a problem with their system.
Does anyone have any experience with issues like this? I would really appreciate any suggestions to help me solve this!

Best regards,
Jolanda