About:

Vitamin k complexes are advised as a synergistic supplement with larger booster doses of vitamin D, as they reduce the potential for hypercalcemia side-effects. In addition it is now known that its importance goes much beyond this.

Vitamin K-dependent matrix Gla protein (MGP) has been extensively studied as an inhibitor of vascular mineralization; however, its role in the pulmonary compartment seems to be comparable. Besides preventing soft tissue calcification, MGP also protects against elastic fibre degradation. Furthermore, sane doses of vitamin K complexes seem quite safe for most people, "vitamin K does not have any known unfavourable effects in those who do not use VKA (Vitamin K antagonists)".

(1). There is a credible mechanism by which the K complexes improve lung conditions in SARS2 infections:

Affinity of elastic fibres for Ca is high. Critically, elastic fibre calcification and proteolytic degradation processes are closely related.

(2). The authors claim some data is suggestive of K deficiency being associated with bad or severe outcomes

Conditions associated with chronic elastic fibre pathology, including diabetes, hypertension and CVD, are also related to worse prognosis of SARS-CoV-2 infection. Recent data demonstrated that Covid-19 patients with poor outcomes had increased thoracic aortic and coronary artery calcification on computed tomography scan, though these analyses lost significance after correction for age and sex. Nevertheless, pre-existing elastic fibre damage predisposes to enhanced proteolytic degradation during inflammation, potentially explaining the increased severity of Covid-19 in those populations.

Their data at this point is lacking for a conclusive answer, but the authors call for a further investigation. They did receive funding from industry.

My take on this is that K is a pretty good idea on any doses much larger than 5000 IU (for adults). So 5000IU with a decent sized meal without K seems fine for most. Could be different for those really low on this nutrient.

Members of the K family are found in greens, as well as fermented foods such as hard cheeses, and perhaps even things like tempeh and kim chi.