I don't know if anything specific has been said about the oil fields, but the issue of Western intervention in Syria (which unlike Russia's doesn't enjoy the approval of the Syrian government) has been discussed quite a bit. This quote from the Parliament of Australia is probably a decent summary of the West's position:
The legality of foreign military activity in Iraq is broadly accepted given that the Iraqi Government’s 2014 invitation requesting assistance provided a clear mandate, or consent. However, the justification for the use of force in Syria is more complex even though it is ostensibly based on the same Iraqi invitation and (albeit expanded) collective self-defence principles. For a number of states, operations in Syria are also a matter of individual self-defence (discussed further below).
The UNSC has not provided any form of explicit legal cover for military operations in Syria as Russia and China, with their veto powers as permanent UNSC members, have opposed any form of Chapter VII mandate. However, a number of resolutions have been passed by the UNSC condemning the violence and urging member states to take all action possible against ISIS, including resolutions 2170, 2178, 2199 and 2249. Resolution 2249 specifically labelled ISIS an ‘unprecedented threat’ and called upon member states with the capacity to do so to take all necessary measures to prevent and suppress the group in Syria and Iraq. Many legal authorities note that the wording of this resolution provided a level of ambiguity on the use of force which could be taken to provide political support for such action, even though the UNSC did not legally endorse such a response. The key text is as follows:
... calls upon Member States that have the capacity to do so to take all necessary measures, in compliance with international law, in particular with the United Nations Charter, as well as international human rights, refugee and humanitarian law, on the territory under the control of ISIL also known as Da’esh, in Syria and Iraq, to redouble and coordinate their efforts to prevent and suppress terrorist acts committed specifically by ISIL also known as Da’esh as well as ANF, and all other individuals, groups, undertakings, and entities associated with Al Qaeda, and other terrorist groups, as designated by the United Nations Security Council, and as may further be agreed by the International Syria Support Group (ISSG) and endorsed by the UN Security Council, pursuant to the Statement of the International Syria Support Group (ISSG) of 14 November, and to eradicate the safe haven they have established over significant parts of Iraq and Syria.
As such, all OIR Coalition members operating in Syria have justified their actions on the basis of the collective self-defence of Iraq, given that ISIS had established bases in Syria which presented a direct threat to the security of Iraq and Iraq invited the US to assist. In a letter to the UNSC the Iraqi representative stated:
As we noted in our earlier letter, ISIL has established a safe haven outside Iraq’s borders that is a direct threat to the security of our people and territory. By establishing this safe haven, ISIL has secured for itself the ability to train for, plan, finance and carry out terrorist operations across our borders. The presence of this safe haven has made our borders impossible to defend and exposed our citizens to the threat of terrorist attacks. It is for these reasons that we, in accordance with international law and the relevant bilateral and multilateral agreements, and with due regard for complete national sovereignty and the Constitution, have requested the United States of America to lead international efforts to strike ISIL sites and military strongholds, with our express consent. The aim of such strikes is to end the constant threat to Iraq, protect Iraq’s citizens and, ultimately, arm Iraqi forces and enable them to regain control of Iraq’s borders.
Another component of this justification is the notion that Syria was unable or unwilling to prevent ongoing armed attacks by ISIS on Iraq, though not all states participating in operations mention this doctrine. As such, other states argue they are justified conducting operations in Iraq’s defence beyond Iraqi borders because they are acting in collective self-defence of Iraq. This raises questions of whether consent could have been obtained from Syria—this was not ruled out by Damascus—or whether the country’s ability to deal with the threat of ISIS may have now changed, although these issues are far too complex to explore in the context of this paper. Any notion of Syria ‘passively consenting’ to Coalition military operations was also dashed when Damascus singled out the US, UK and Australia for conducting air strikes in what they regard as a blatant violation of Syrian sovereignty, and the Syrian Foreign Minister stated on 6 February 2016 that any foreign ground troops entering Syria would ‘return home in wooden coffins’.
The US, UK, France and Turkey have also used an additional, individual self-defence justification, noting that the presence of terrorist groups in Syria is a direct threat to their homelands. The US stated as much in 2015 following strikes against the Khorasan Group (although it has since referenced self-defence in a broader context). The UK did the same following an air strike it conducted on a British citizen in 2015, as did France following the Paris attacks.
To the extent that the lastest action of the US is directed against the oil fields falling in ISIS hands again, it could be justified under the same principles.