Whether to control the oil or flat out take the oil, US statements on the new military mission in Syria are heavily oil-themed. Other reports, however, suggest that the operation is a lot more complicated than that.
In reality, a lot of the goal is nation-building, with US forces meant to both keep the Syrian government out of this part of Syria, and try to “bring prosperity” to the region, propping up a potential territory of rebels.
This is again built around the assumption that the US can manufacture an autonomous, prosperous region, using the oilfields as the revenue source, and then steer that region toward hostility with the rest of Syria.
This will likely end up being a plan easier for the Trump Administration to sell than overt theft of oil, as it allows the US to retain its primary focus, military hostility toward Syria with an eye toward eventual regime change.
To that end, the US keeps condemning Syria and Russia for airstrikes in the Idlib Province of northwestern Syria, and is demanding a full halt to strikes to resolve the situation through the UN. Ironically, the US has also opposed that UN reconciliation process, because it’s not going to end with regime change.
Pentagon officials are also pointing out that their military presence in Syria implies US military authority to open fire on Syrian government representatives if any of them try to reclaim control over the Syrian oilfields.