Shall I quote the very first line of your post?
“These ‘scientists’ claim this object is approximately ‘35,000,000 years old; but then later try to tell us it originated from a hydrogen cloud 100 to 160 million light years away???!!!!”
You later refer to the person writing the article - but not in your opening line. You clearly refer to the scientists in it. It is the second word in your post.
Hence why you appear confused.
” Of these 6 young associations, only CAR and COL intersect with ‘Oumuamua’s trajectory at their corre- sponding ages of 30 and 42 Myr. In particular, the CAR association appears to move in concert with ‘Oumuamua and maximizes its 1-σ intersection volume with the ISO at around 34 Myr. The 34 Myr peak of CAR’s inter- section volume is in agreement with the ∼25-30 Myr old age based on lithium depletion method and its color magnitude diagram (Schneider et al. 2019). COL while also intersecting with the ISO, does not maximize its 1-σ intersection volume at 42Myr. This suggests that ‘Oumuamua more likely originated from CAR than from COL.
…
We obtain ejection speeds of 1.67 km s−1 and 0.85 km s−1 for CAR(ina) and COL(umba) respectively. We note that the current position of ‘Oumuamua is closer to the cluster center than the furthest association star for both CAR and COL, which would be expected for a member of either of these associations, and the modest speed is consistent with both the disk ejection and molecular cloud byproduct hypotheses (Gaidos et al. 2017; Seligman & Laughlin 2020).
An order-of-magnitude estimate seems to distinguish between the scenarios. Using the Do et al. (2018) estimate of 4 M⊕ pc−3, and spherical volumes defined by the furthest member in the cluster (∼ 55pc for CAR, ∼ 70 pc for COL, see Figure 6), one finds a combined volume for CAR and COL of ∼ 2.1 × 106 pc3. Naively, this implies an enormous total of ∼ 8.5×106 M⊕ in ‘Oumuamua-like objects originating from CAR and COL.”
The authors also admit the extreme difficulty of formation of hydrogen ice in the proposed conditions — most theoretical proposals for solid forms of hydrogen require low temperature and extreme high pressure, which would not exist in the clouds proposed, but might be found in the cores of gas giant planets— and suggest a fallback proposal of nitrogen ice for ‘Oumuamua.
Now, for the math… if we assume a velocity of 200,000 MPH for 100 light years (accepting your distance to the Carina Group) from the closest edge of that group of stars, then ‘Oumuamua could make ~335,538years, give or take a few hundred thousand for wandering around inside the group before being squirted out.
My point is that papers like this are all speculation built on minimal data, with very little to build their case on. They’re a house of cards built on similar papers built on similar lack of data. For example the "age" is assumed by the amount of Lithium in relation to Hydrogen but they aren’t sure of the hydrogen or the lithium as they admit they have ZERO out gassing and only reflected spectra to work on, AND they assumption extend to a thoroughly theoretical modality of object creation. This results in a question begging conclusion chasing circular reasoning where they prove their beginnings and endings in a circular roundabout.