Thanks for the additional context.  So, if I understand this correctly, it's established that all accounts are now under Gmail and there's no problem accessing all the associated products, including Intuit Link, and you are even able to see all the historical data in Intuit Link going back 10 years or so.

If my understanding is correct, it sounds like your accounts are correctly updated for your login credentials with the new Gmail addresses and it's something else that may be causing the problems you encounter.

I also don't agree with the person who told you that Gmail isn't compatible with Intuit Link because there are plenty of Intuit Link users out there, accountants included (I'd presume), who use Gmail.

Can you confirm whether you have the same problem with both new and old clients?  Also, did you send those invites from ProSeries (which you do for new clients) or within Intuit Link?