How to pause throttling and blocking of out-of-date on-premises Exchange Servers

I'm investigating a problem with a system which should have been migrated a long time ago but wasn't. Its a hybrid Exch2010 <->o365 installation. The exchange server had three domains configured on it. 98% of the users were migrated a long time back but one of the domains remained, for varios reasons.

Mail flow goes through a connector which has a certificate for *.domainA.com. The corresponding connector in o365 has DomainA.com, DomainB.Com and DomainC.com enabled for reception.

All of DomainA users were migrated, apart from a couple of test mailboxes. If I migrate a single DomainB mailbox, I hit the following:

- They cannot receive email from the outside world (it says the connector has been throttled)

- Internal mails work from DomainA.com

- Internal mails work from DomainB.com 

I can send internal mails to any mailbox.

If I use a mailbox in DomainA, but on the exch2010 server,  I can send to users in o365 without any issues - so the connector is not throttling.

Any ideas?