Excellent question! Always glad to see players interested in the story and plot behind a campaign.
So the GVTI engaged in some political back-channel maneuvers to persuade the Gateway Project and Delta Serpentis to drop their objections.
Do you think the conversation went something like this (GTVI representative and Delta Serpentis governor):
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GTVI: Governor, there are reasons to stabilize the Marnakh Knossos asap.
DS: I'm not against scientific research, but returning to Sol has been a dream of our species for decades. We're getting closer and making real progress and now you want to snatch that away so Vasudans can do some exploring?
GTVI: It's not some meaningless scientific expedition. Limited scans so far show massive resources there and potential planets that are livable. We'd be able to settle all the remaining Capella refugees and find the Vasudans a new homeworld. After the NTF war, it's important to maintain good Terran-Vasudan relations and this could go a long way for that.
DS: Look, that may all be true and I'm not saying we should never help the situation in Marnakh. Think though of the economic benefits to our species though that getting Earth back would bring. I'm sure there'd be a place for the Capellans there too.
GTVI: Governor, as you know this conversation between you and I is highly classified. What I'm about to tell you is even more classified. There have been a small number of Shivans spotted in Marnakh. It's important we find out if more are there.
DS: They could be in Sol for all we know too but that's a risk we're willing to take!
GTVI: I'll be frank, the GTVI sees this as more of an immediate priority. To be honest, this is the path we're going to go down and I'm here largely as a courtesy to you.
DS: I'll take this matter to the General Assembly! Other Terrans won't take so kindly to having our homeworld snatched away because of politics.
GTVI: Governor, I would highly advise against that. The Security Council will make sure this happens.
DS: We're never going back to Earth...is that what you're saying?
GTVI: Not at all, not at all. In fact, if you drop your protest in the General Assembly, we can make things better for you and we could get back to Earth sooner than you think perhaps.
DS: I'm listening...
GTVI: We are prepared to make some concessions in exchange for you and the Gateway Project officially dropping your objection to the temporary reallocation of resources from Gateway to Marnakh. One: once these systems are clear of Shivans we can begin bringing in large numbers of workers to begin extracting resources and to build shipyards and facilities in Marnakh and beyond. We could have a large number of these workers be Delta Serpentis companies. Governor, you're up for re-election soon. Thousands of new jobs for people in your system would be quite helpful for that wouldn't you say?
Two: When the GTVA gets new resources, they get split up among Terrans and Vasudans to a certain extent. We'll arrange it so that the first priority of the Terran side of these gains from these new systems will be to replenish and continue Gateway. What say you?
DS: I think we might have a deal here.
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Basically, by back channel maneuvers, you mean the GTVA probably had to offer Delta Serpentis something (at least in secret) to drop its official objections right (and didn't just dictate things)?