Weird issue when sending invites to Gmail

I currently use Zimbra desktop app (7.2.3 GA build 11971). I've learned that companies like Uber, Door3, and Unitas Global who use Gmail do not receive my calendar invites but receive my email fine. I can make the assumption that anyone using (corporate) Gmail will not receive my calendar invites from Zimbra.

However, I just tried sending a calendar invite through Outlook to Door3 and it worked fine but then I would have to maintain two Calendars since they don't sync. Anyone else seeing this problem? How do I fix it?

Thanks!