Andy, maybe I'm a dummy, but I fail to understand what you are talking about.
I THINK you're saying that you created a (3rd party) App which is not part of Groups.io, and its purpose is to receive emails from a group, and present them to the member in a form other than email. I think you are asking for a way for Groups.io to continue feeding those emails to your App, but not send them to the member in the form of emails. How badly have I misunderstood?
On the off-hand chance that I actually understood, then I see 3 choices. (1) Ask Mark to add a new feature to Groups.io to send group messages specifically to your App (or to some class of Apps of which yours is one), and let the user select whether to receive messages through that new port, or emails, or both, or neither. (2) Let the user set up their email system to automatically delete emails from the group. Gmail lets you do that. (3) Tell the member to subscribe twice, set their normal groupts.io account to No Email, and let the other account send messages to your App.
I think you've left us somewhat in a fog about your App and that may be part of the problem with your question.
Andy (the other one)