I kind of want to know how they safely deal with its release (destruction)
Ejecting the warp core is a common strategy.
E=mc*2 but m is really really tiny
If it's a single particle I don't think there's much to worry about?
In addition to knowing how much stuff is released by one particle, we have a decent handle on how much is needed in order to be dangerous, due to us being constantly bombarded by various cosmic rays. That's how we can say that it's not dangerous.
The article is behind a paywall, but it seems likely that the bigger safety concern is whatever produced the large quantity of particles needed to have a chance of trapping just one. And those kinds of experiments are conducted in regulated facilities for good reason.
As the sibling comments say, it's a single positron so the energy released is tiny. I tried to find positrons sources in common life, the best I could find was https://en.wikipedia.org/wiki/Positron_emission_tomography The relevant paragraph are
> For a typical dose (245 MBq) of FDG, one of the most common radiotracers used for PET neuroimaging and cancer patient management,[48] the effective radiation dose is 4.7 mSv.[49]
and
> This limitation restricts clinical PET primarily to the use of tracers labelled with fluorine-18, which has a half-life of 110 minutes and can be transported a reasonable distance before use.
Where "245 MBq" means 2*10^8 positrons per second for. And "110 minutes" means a half disappears every 2 hours, so the total sum is equivalent to 4 hours but I'm missing some small constant and they ae probably averaging the dose. I guess "3 hours" is a good compromise but multiply it by 2 or 4 if you prefer a smaller or bigger number. Anyway, 3 hours are 10^4 seconds, so the total numbers of positrons in a PET is approximately 2*10^8 * 10^4 = 2*10^12.