I have discussed this with your team, but wanted to put an Idea post out there.
Currently, Emma's Response API only includes the Mailing ID for the 'Delivered' type. We have a request out to Emma to include this on the other Response Types.
However, I was wondering if it was possible to snag the Mailing ID from the API call itself as a work around? Since the calls are structured as: "/#account_id/response/#mailing_id/[type]", would it be possible to save the mailing_id used in the call and use that to surface the ID in the Emma Connector as a workaround in the meantime?
I wanted to let you know that my team will be investigating this request to implement during the second half of this year. I may reach back out to you if we have questions and will update you once it is implemented.