The load-bearing claim in the SHIELD work is geometric before it is climatic. If an interstellar cold cloud compresses the heliosphere to less than the radius of Earth's orbit, the planet is not partially screened, it is outside the screen entirely, with its atmosphere meeting the cloud directly [4]. NASA's own account keeps the climate step conditional throughout: the environments the heliosphere crossed may have triggered changes on Earth, and the collapse events may explain some ancient climatic patterns, including possible ice ages [8].
Put the three windows on a timeline and a second constraint appears. Taking the midpoints at 2.5, 6.5 and 13.5 million years ago gives gaps of roughly four and seven million years, about one encounter per 4.5 million years across the interval [16]. The same release describes ice ages in which global average temperature dropped several degrees and during which warming and cooling swings became more frequent [10]. An external forcing that arrives twice per ten million years cannot pace swings like that. It can move the baseline they oscillate around, which is a different job.
The simulated mechanism is also less specific than the headline suggests. Exposure to a cold, dense galactic hydrogen cloud raised atmospheric water vapor content and shifted upper-atmospheric dynamics, and the account stops at "altering the conditions at the surface" [7]. No sign, no magnitude, no duration. Water vapor is itself a greenhouse gas, so a stated increase in it is not on its own a cooling mechanism, and the route from upper-atmosphere dynamics to surface temperature is exactly the part a paleoclimate modeller would need quantified.
The young Sun paper has a sharper problem and a thinner public description. Three billion years ago, according to Goddard's Vladimir Airapetian, the Sun was 70% as bright as today, which should have left Earth frozen solid, and yet geological evidence shows stable liquid water existed well before that [13][14]. That is a 30% shortfall in output [17], at a point when the Sun was about 1.6 billion years old, roughly 35% of its present age [18]. NASA describes the proposed fix in one clause: the dimmer young Sun heated Earth by seeding the production of potent greenhouse gases [15]. Which gas, at what mixing ratio, produced by superflares at what frequency, are the three numbers that would make the idea testable against the Archean record, and the summary carries none of them.
What the two studies jointly propose is that the galactic environment stops being a constant in Earth-system reconstruction and becomes an input with a history [1]. That is a reasonable thing to propose. It is not yet a term anyone can put a coefficient on.
