How to pause throttling and blocking of out-of-date on-premises Exchange Servers

mkcj1984 - when you set up an inbound connector in EXO the ConnectorType property was set to either OnPremises or Partner. If you're sending mail over an EXO inbound connector from your on-prem environment then the connector type would have (should have) been set to "OnPremises". Inbound connectors where ConnectorType is "Partner" are for trusted mail flow from a business partner or a 3rd party smarthost or service. A connecting Exchange server over a "Partner" inbound connector likely doesn't belong to you or isn't in your control, so we don't include them as part of the enforcement scope. At this time the enforcement scope is just those out-of-date Exchange servers connecting via an inbound connector of type "OnPremises". 

You can check your inbound connector type(s) by connecting to Exchange Online PowerShell (Connect-ExchangeOnline) and then running:

Get-InboundConnector | ft Name, Connectortype